Paper Citation Record · LEDGER

The existence of a nontrivial weak solution to a double critical problem involving fractional Laplacian in ${\R}^n$ with a Hardy term

As of 22 August 2026, this Paper Citation Record lists 45 of 45 outbound references and 0 inbound Pith citation observations for arXiv:1908.02536.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
1908.02536 v2

Coverage vector

measured 45 of 45 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T14:56:58.043053Z

measured 45 of 45 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

45 of 45 outbound references displayed

verified exact3
verified fuzzy24
unresolved18
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 43528f31-fab9-42e2-8d33-39489b0a1677 · outbound

This paper cites Br´ezis, L.

The existence of a nontrivial weak solution to a double critical problem involving fractional Laplacian in ${\R}^n$ with a Hardy term Br´ezis, L

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:56:58.475737Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 40a3f29a-cc8c-4e89-923e-a52d1f68e6fd · outbound

This paper cites Ghoussoub, S.

The existence of a nontrivial weak solution to a double critical problem involving fractional Laplacian in ${\R}^n$ with a Hardy term Ghoussoub, S

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:56:58.466606Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 7e9f2c2a-e5b2-4f85-bd57-ed9e7d21e754 · outbound

This paper cites Dipierro , L.

The existence of a nontrivial weak solution to a double critical problem involving fractional Laplacian in ${\R}^n$ with a Hardy term Dipierro , L

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:56:58.457557Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation a72c3ac9-1727-49d0-8dae-7f2f09464fd1 · outbound

This paper cites Palatucci, A.

The existence of a nontrivial weak solution to a double critical problem involving fractional Laplacian in ${\R}^n$ with a Hardy term Palatucci, A

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:56:58.448811Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 6d008e20-5dd0-4933-850f-7982099b16de · outbound

This paper cites Komori, S.

The existence of a nontrivial weak solution to a double critical problem involving fractional Laplacian in ${\R}^n$ with a Hardy term Komori, S

Reference 5

Resolution: verified exact; doi, observed 2026-08-14T14:56:58.083571Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 138fdf92-c0c6-446c-8bec-cb7ba01b2a6e · outbound

This paper cites an unresolved cited work.

The existence of a nontrivial weak solution to a double critical problem involving fractional Laplacian in ${\R}^n$ with a Hardy term Unresolved cited work

Reference 6

Resolution: verified exact; doi, observed 2026-08-14T14:56:58.073395Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 8d6a6378-0a34-4212-86e2-0a35c863716a · outbound

This paper cites an unresolved cited work.

The existence of a nontrivial weak solution to a double critical problem involving fractional Laplacian in ${\R}^n$ with a Hardy term Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-14T14:56:58.440484Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation aff47c02-681d-4188-a45a-3decaa49a272 · outbound

This paper cites Muckenhoupt, R.

The existence of a nontrivial weak solution to a double critical problem involving fractional Laplacian in ${\R}^n$ with a Hardy term Muckenhoupt, R

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:56:58.431994Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 87155c82-12eb-42e3-8865-bfd6278cb81f · outbound

This paper cites Catrina, Z.

The existence of a nontrivial weak solution to a double critical problem involving fractional Laplacian in ${\R}^n$ with a Hardy term Catrina, Z

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:56:58.423511Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 613d250c-3ea1-4008-8500-6fb3ae4fcd7e · outbound

This paper cites an unresolved cited work.

The existence of a nontrivial weak solution to a double critical problem involving fractional Laplacian in ${\R}^n$ with a Hardy term Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-14T14:56:58.414660Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 1ebe5191-e96a-4958-95ef-d7a562086fe9 · outbound

This paper cites Ghoussoub, C.

The existence of a nontrivial weak solution to a double critical problem involving fractional Laplacian in ${\R}^n$ with a Hardy term Ghoussoub, C

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:56:58.405736Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation dea35ce2-f5c8-4151-8b17-d58437c99c74 · outbound

This paper cites Ghoussoub, A.

The existence of a nontrivial weak solution to a double critical problem involving fractional Laplacian in ${\R}^n$ with a Hardy term Ghoussoub, A

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:56:58.396640Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 662d6fb0-1763-4a51-af34-5622346004dd · outbound

This paper cites Ghoussoub, F.

The existence of a nontrivial weak solution to a double critical problem involving fractional Laplacian in ${\R}^n$ with a Hardy term Ghoussoub, F

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:56:58.387702Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation df8461f6-97b0-4453-9fc2-0d4a064d0ffc · outbound

This paper cites Ghoussoub, F.

The existence of a nontrivial weak solution to a double critical problem involving fractional Laplacian in ${\R}^n$ with a Hardy term Ghoussoub, F

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:56:58.378556Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 4ce43a0d-5574-4e99-8580-5037a60c846b · outbound

This paper cites Lei, Asymptotic properties of positive solutions of the Hardy -Sobolev type equations, J.

The existence of a nontrivial weak solution to a double critical problem involving fractional Laplacian in ${\R}^n$ with a Hardy term Lei, Asymptotic properties of positive solutions of the Hardy -Sobolev type equations, J

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:56:58.369323Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 98a7cb00-f2be-4df2-9646-a8e199940f8b · outbound

This paper cites an unresolved cited work.

The existence of a nontrivial weak solution to a double critical problem involving fractional Laplacian in ${\R}^n$ with a Hardy term Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-14T14:56:58.360031Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation e6bf661e-1ceb-492b-a735-4eb4a01fff88 · outbound

This paper cites an unresolved cited work.

The existence of a nontrivial weak solution to a double critical problem involving fractional Laplacian in ${\R}^n$ with a Hardy term Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-14T14:56:58.351163Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 8dd6cca2-fae9-490e-9b0b-3b898aa98593 · outbound

This paper cites an unresolved cited work.

The existence of a nontrivial weak solution to a double critical problem involving fractional Laplacian in ${\R}^n$ with a Hardy term Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-14T14:56:58.341743Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation f31d4560-e1b0-4b31-a4a8-8b4676b8ceb1 · outbound

This paper cites an unresolved cited work.

The existence of a nontrivial weak solution to a double critical problem involving fractional Laplacian in ${\R}^n$ with a Hardy term Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-14T14:56:58.332238Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation d190d740-8aab-43ed-8ca9-219f49d18cbb · outbound

This paper cites Filippucci, P.

The existence of a nontrivial weak solution to a double critical problem involving fractional Laplacian in ${\R}^n$ with a Hardy term Filippucci, P

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:56:58.323108Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 2983dbec-96bc-46ae-9ca3-aa55ca5d40ac · outbound

This paper cites an unresolved cited work.

The existence of a nontrivial weak solution to a double critical problem involving fractional Laplacian in ${\R}^n$ with a Hardy term Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-14T14:56:58.314485Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 4f4513f4-907c-43d6-9af6-43a3b8c79f75 · outbound

This paper cites Caﬀarelli, L.

The existence of a nontrivial weak solution to a double critical problem involving fractional Laplacian in ${\R}^n$ with a Hardy term Caﬀarelli, L

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:56:58.305679Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 90792d96-7dd2-4a72-bc37-4f215c289839 · outbound

This paper cites an unresolved cited work.

The existence of a nontrivial weak solution to a double critical problem involving fractional Laplacian in ${\R}^n$ with a Hardy term Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-14T14:56:58.297125Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 8587cb73-cb9c-4aa1-884a-1dea740b6404 · outbound

This paper cites Terracini, On positive entire solutions to a class of equations w ith a singular coeﬃcient and critical exponent, Adv.

The existence of a nontrivial weak solution to a double critical problem involving fractional Laplacian in ${\R}^n$ with a Hardy term Terracini, On positive entire solutions to a class of equations w ith a singular coeﬃcient and critical exponent, Adv

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:56:58.288086Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation f6204f4b-2d2f-40fe-b828-aae7dcfd0d68 · outbound

This paper cites an unresolved cited work.

The existence of a nontrivial weak solution to a double critical problem involving fractional Laplacian in ${\R}^n$ with a Hardy term Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-14T14:56:58.278879Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation b287ae72-db69-4017-ae46-fff7997d28ec · outbound

This paper cites an unresolved cited work.

The existence of a nontrivial weak solution to a double critical problem involving fractional Laplacian in ${\R}^n$ with a Hardy term Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-14T14:56:58.269123Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 3e3e08bb-a0d4-4bab-baeb-1f67b8c35442 · outbound

This paper cites an unresolved cited work.

The existence of a nontrivial weak solution to a double critical problem involving fractional Laplacian in ${\R}^n$ with a Hardy term Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-14T14:56:58.260170Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 4baf9882-47cc-412b-bfa7-5cc30044b0da · outbound

This paper cites an unresolved cited work.

The existence of a nontrivial weak solution to a double critical problem involving fractional Laplacian in ${\R}^n$ with a Hardy term Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-14T14:56:58.251292Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 744196fc-e099-4f85-aabe-59431e13efcf · outbound

This paper cites Sawyer, R.

The existence of a nontrivial weak solution to a double critical problem involving fractional Laplacian in ${\R}^n$ with a Hardy term Sawyer, R

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:56:58.242408Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 3c57537c-590b-4068-9f39-fe900b5b6662 · outbound

This paper cites Yang, Fractional Hardy-Sobolev inequality in RN , Nonlinear Analysis: Theory, Methods and Applications.

The existence of a nontrivial weak solution to a double critical problem involving fractional Laplacian in ${\R}^n$ with a Hardy term Yang, Fractional Hardy-Sobolev inequality in RN , Nonlinear Analysis: Theory, Methods and Applications

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:56:58.233660Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation f8c5a7f8-87af-4ada-bba2-5ad4a22fde22 · outbound

This paper cites Chen, Fractional elliptic problems with two critical Sobolev-Ha rdy exponents, Electronic Journal of Diﬀerential Equations 2018(2018).

The existence of a nontrivial weak solution to a double critical problem involving fractional Laplacian in ${\R}^n$ with a Hardy term Chen, Fractional elliptic problems with two critical Sobolev-Ha rdy exponents, Electronic Journal of Diﬀerential Equations 2018(2018)

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:56:58.225147Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 3c2a34ce-a074-4bf2-86bf-b556253de48a · outbound

This paper cites Servadei, E.

The existence of a nontrivial weak solution to a double critical problem involving fractional Laplacian in ${\R}^n$ with a Hardy term Servadei, E

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:56:58.216003Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation e452fce8-8aa3-4b7c-acb2-8f41e93ed1fd · outbound

This paper cites an unresolved cited work.

The existence of a nontrivial weak solution to a double critical problem involving fractional Laplacian in ${\R}^n$ with a Hardy term Unresolved cited work

Reference 33

Resolution: unresolved; raw_fallback, observed 2026-08-14T14:56:58.207231Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation b33e91c9-f0d8-408a-ad1b-1da2b44df34c · outbound

This paper cites an unresolved cited work.

The existence of a nontrivial weak solution to a double critical problem involving fractional Laplacian in ${\R}^n$ with a Hardy term Unresolved cited work

Reference 34

Resolution: unresolved; raw_fallback, observed 2026-08-14T14:56:58.198235Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 506d9a95-c8cd-416a-9beb-a7ae75c677b4 · outbound

This paper cites an unresolved cited work.

The existence of a nontrivial weak solution to a double critical problem involving fractional Laplacian in ${\R}^n$ with a Hardy term Unresolved cited work

Reference 35

Resolution: unresolved; raw_fallback, observed 2026-08-14T14:56:58.189422Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 1e6f3690-242f-492c-a14f-8d0c833df1a6 · outbound

This paper cites Brezis, E.

The existence of a nontrivial weak solution to a double critical problem involving fractional Laplacian in ${\R}^n$ with a Hardy term Brezis, E

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:56:58.180754Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 8fe74270-bb6f-4b75-b302-0aa98e87aeed · outbound

This paper cites Ambrosetti, P.

The existence of a nontrivial weak solution to a double critical problem involving fractional Laplacian in ${\R}^n$ with a Hardy term Ambrosetti, P

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:56:58.171656Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 006d4e3d-e2f7-49b6-bf03-f6f9a6dbbdc3 · outbound

This paper cites Moroz, J.

The existence of a nontrivial weak solution to a double critical problem involving fractional Laplacian in ${\R}^n$ with a Hardy term Moroz, J

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:56:58.163271Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation de8a2032-4ea1-4d0f-a0a7-c5ac78af6e2a · outbound

This paper cites Huang, D.

The existence of a nontrivial weak solution to a double critical problem involving fractional Laplacian in ${\R}^n$ with a Hardy term Huang, D

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:56:58.154590Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation a6f2b94f-1f93-4698-bc9c-8993c03f7932 · outbound

This paper cites an unresolved cited work.

The existence of a nontrivial weak solution to a double critical problem involving fractional Laplacian in ${\R}^n$ with a Hardy term Unresolved cited work

Reference 40

Resolution: unresolved; raw_fallback, observed 2026-08-14T14:56:58.145354Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 97078edd-117e-4c7e-baad-6ebb8d29bc48 · outbound

This paper cites an unresolved cited work.

The existence of a nontrivial weak solution to a double critical problem involving fractional Laplacian in ${\R}^n$ with a Hardy term Unresolved cited work

Reference 41

Resolution: unresolved; raw_fallback, observed 2026-08-14T14:56:58.136377Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 60e9cef1-7d0d-428c-9f35-62cc02bf12d4 · outbound

This paper cites an unresolved cited work.

The existence of a nontrivial weak solution to a double critical problem involving fractional Laplacian in ${\R}^n$ with a Hardy term Unresolved cited work

Reference 42

Resolution: unresolved; raw_fallback, observed 2026-08-14T14:56:58.126257Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation c00593a8-e742-4f18-bce0-39d8f0aad504 · outbound

This paper cites Villavert.

The existence of a nontrivial weak solution to a double critical problem involving fractional Laplacian in ${\R}^n$ with a Hardy term Villavert

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:56:58.117237Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation e96d4f5c-beeb-4f0d-b1e6-99ac33026b56 · outbound

This paper cites Nursultanov, S.

The existence of a nontrivial weak solution to a double critical problem involving fractional Laplacian in ${\R}^n$ with a Hardy term Nursultanov, S

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:56:58.107406Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 03a52b9a-4420-43a5-b4df-ab2f3119ddf3 · outbound

This paper cites Nonlocal Pertubations of Fractional Choquard Equation.

The existence of a nontrivial weak solution to a double critical problem involving fractional Laplacian in ${\R}^n$ with a Hardy term Nonlocal Pertubations of Fractional Choquard Equation

Reference 45

Resolution: verified exact; local_arxiv, observed 2026-08-14T14:56:58.097232Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Pith citing papers

No inbound Pith citation observations are available.