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Paper Citation Record · LEDGER

Existence and convergence of solutions for nonlinear biharmonic equations on graphs

As of 16 August 2026, this Paper Citation Record lists 33 of 33 outbound references and 0 inbound Pith citation observations for arXiv:1908.03993.

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

pith.paper-citation-record.v1
1908.03993 v1

Coverage vector

measured 33 of 33 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T14:11:10.163214Z

measured 33 of 33 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+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

33 of 33 outbound references displayed

  • verified exact1
  • verified fuzzy26
  • unresolved6
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 9451530e-8b51-4b9a-a52c-6d4ec1bc5ab6 · outbound

This paper cites Abrahams, A.M.

Existence and convergence of solutions for nonlinear biharmonic equations on graphs Abrahams, A.M

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:11:10.937696Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

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Observation a73da688-6647-4072-84ce-57ab9fd2aee0 · outbound

This paper cites Alves, M.A.S.

Existence and convergence of solutions for nonlinear biharmonic equations on graphs Alves, M.A.S

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:11:10.915290Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:09.946352Z digest=sha256:ecbaf120dce07eacdc12f66577beafc6e2b5709f4152ffc3942b6f6ddb722d1e

Observation d5cf1fba-2db7-4eb3-87df-05c8c64bedf1 · outbound

This paper cites Arnaboldi, A.

Existence and convergence of solutions for nonlinear biharmonic equations on graphs Arnaboldi, A

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:11:10.887858Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:09.951962Z digest=sha256:5aae7c2d7a6febad66763caa1c35c795292cf0445f3ab64408ce1ce36516f6af

Observation e5a8c360-33d1-486a-b7e6-53ebba813455 · outbound

This paper cites Bartsch, Z.Q.

Existence and convergence of solutions for nonlinear biharmonic equations on graphs Bartsch, Z.Q

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:11:10.869200Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:09.960094Z digest=sha256:caca1d188ff99e48bd2d33466610e0a3fe772f3386cc6365f71529de45dd98ed

Observation e6a3ba3a-01e3-47c0-bbf2-510251be6131 · outbound

This paper cites an unresolved cited work.

Existence and convergence of solutions for nonlinear biharmonic equations on graphs Unresolved cited work

Reference 5

Resolution
unresolved
raw_fallback, observed 2026-08-14T14:11:10.853385Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:09.965467Z digest=sha256:a213090250d7c6ef7aafa0f4d7db05e92a21d8c028d655491cdb620c3c5c1aff

Observation 16419997-64b1-4b37-80b1-509916a7d576 · outbound

This paper cites Br´ ezis, L.

Existence and convergence of solutions for nonlinear biharmonic equations on graphs Br´ ezis, L

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:11:10.838557Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:09.971162Z digest=sha256:606a2c103c9025320c7455f612bdf1c23eea4859a9395588b03ff1a07a269988

Observation f562cb41-bf46-427f-9942-51ddecaba94a · outbound

This paper cites Cao, Nontrivial solution of semilinear equations with critical ex ponent in R2, Commun.

Existence and convergence of solutions for nonlinear biharmonic equations on graphs Cao, Nontrivial solution of semilinear equations with critical ex ponent in R2, Commun

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:11:10.821597Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:09.977354Z digest=sha256:4e7b2fed62453118889328aa208a02e65d76a9313a9b6c324c9f2bcdcabc1712

Observation ce0f13ec-a1c3-4076-8cbb-d50c2c4c7e92 · outbound

This paper cites an unresolved cited work.

Existence and convergence of solutions for nonlinear biharmonic equations on graphs Unresolved cited work

Reference 8

Resolution
unresolved
raw_fallback, observed 2026-08-14T14:11:10.793903Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:09.984516Z digest=sha256:d95a068c50cf6b447a7cf8390e5f6566d2c3ac14f95adc19e7092cd73eaeea58

Observation 9a0dd9f8-4715-46b5-a736-b3be9a476507 · outbound

This paper cites an unresolved cited work.

Existence and convergence of solutions for nonlinear biharmonic equations on graphs Unresolved cited work

Reference 9

Resolution
unresolved
raw_fallback, observed 2026-08-14T14:11:10.765772Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:09.993746Z digest=sha256:e875ce0fdc3915d05bcc2d2a1cd58af08eb17f84cd02ca6413e74e25041c8a77

Observation 615a6c2f-f0eb-4678-91de-601131d4cb4e · outbound

This paper cites Grigor’yan, Y.

Existence and convergence of solutions for nonlinear biharmonic equations on graphs Grigor’yan, Y

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:11:10.748758Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:10.004403Z digest=sha256:30634619f14484a27737d271d15883b85697d7d885a0ae075f3ad920b3fa46f8

Observation 92a75003-025a-425f-b992-a05fc22ebafb · outbound

This paper cites Grigor’yan, Y.

Existence and convergence of solutions for nonlinear biharmonic equations on graphs Grigor’yan, Y

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:11:10.730536Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:10.010788Z digest=sha256:b0e2cc08fa334e7555740a74d3b4364b55d602bd886fa3dc61dac59a439ff697

Observation 59d837a1-6200-4d19-bd50-a701de15459b · outbound

This paper cites Grigor’yan, Y.

Existence and convergence of solutions for nonlinear biharmonic equations on graphs Grigor’yan, Y

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:11:10.708946Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:10.017532Z digest=sha256:477ca85b53a8cb5c7b66443418a4f517b58ddce3b3890c0183d2d6a8fa04791d

Observation 9574c341-26af-45cf-8015-9c5fa076c0b6 · outbound

This paper cites an unresolved cited work.

Existence and convergence of solutions for nonlinear biharmonic equations on graphs Unresolved cited work

Reference 13

Resolution
unresolved
raw_fallback, observed 2026-08-14T14:11:10.674210Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:10.025976Z digest=sha256:810fbb41bcab793c40cccfab64b00d1b8ee6da3efc86462ef13755a69e3002de

Observation cb1bf5bf-7b22-4489-a52b-3633f5451400 · outbound

This paper cites an unresolved cited work.

Existence and convergence of solutions for nonlinear biharmonic equations on graphs Unresolved cited work

Reference 14

Resolution
verified exact
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:10.034678Z digest=sha256:08a1bce44702b11a7bdff6b40c87733d518be3a95d8f29702cfe27328c5a77c1

Observation 0da60ce5-fd68-4e3d-a185-6085a274958c · outbound

This paper cites an unresolved cited work.

Existence and convergence of solutions for nonlinear biharmonic equations on graphs Unresolved cited work

Reference 15

Resolution
unresolved
raw_fallback, observed 2026-08-14T14:11:10.651249Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:10.041911Z digest=sha256:84f3090a7171d4686cef370d3061bc00870dc8d429646b62b1c76ad67f3f28ab

Observation eab4e803-5148-4686-9cb4-3bf264630dc0 · outbound

This paper cites Huang, On uniqueness class for a heat equation on graphs, J.

Existence and convergence of solutions for nonlinear biharmonic equations on graphs Huang, On uniqueness class for a heat equation on graphs, J

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:11:10.632429Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:10.047147Z digest=sha256:536e0e774f90c2e54a1a2b3bf0afd9ef8a446b9d470039ba633ae4558ebd67b0

Observation 691a66f7-f302-4373-90ce-6fcfb7ee953a · outbound

This paper cites Huang, M.

Existence and convergence of solutions for nonlinear biharmonic equations on graphs Huang, M

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:11:10.608673Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:10.053174Z digest=sha256:6dc83f3c52512eed8431aeb2373d2a4b71906abb1354245a07ca00dcf7ac1e23

Observation a6440e85-0241-42ce-b2d3-80cf36ba925a · outbound

This paper cites Keller, M.

Existence and convergence of solutions for nonlinear biharmonic equations on graphs Keller, M

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:11:10.586372Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:10.058189Z digest=sha256:b3d6b91e4386eaa1dc3b6d301c89c7ae7758a02bf1d6891600c14217e99a5b95

Observation e530f135-efc5-4af2-b32f-01b300b018ba · outbound

This paper cites Lezoray, L.

Existence and convergence of solutions for nonlinear biharmonic equations on graphs Lezoray, L

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:11:10.566541Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:10.063814Z digest=sha256:168f364408a20f2896ebade74ac697aa293dfb09e6a52e88b39d1626a384ae99

Observation 60686cff-0e47-4bf6-8e2b-23ec757b6d5b · outbound

This paper cites Lin, Y.T.

Existence and convergence of solutions for nonlinear biharmonic equations on graphs Lin, Y.T

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:11:10.551095Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:10.068522Z digest=sha256:f022297ef0a49330f9ad13beaa27d46fe630c3ed069ad1743ae22628dac14f4b

Observation 2b2bc51b-fac6-46eb-ad49-c772d2113b63 · outbound

This paper cites Liu, H.B.

Existence and convergence of solutions for nonlinear biharmonic equations on graphs Liu, H.B

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:11:10.532927Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:10.075701Z digest=sha256:c0e0e8630bf24bff6d1769e54dc1ef68aad86bd7dc1bba75c9511e8b8e9e4b30

Observation 5fd70685-101e-4dca-9e54-74108bccd92d · outbound

This paper cites Liu, K.W.

Existence and convergence of solutions for nonlinear biharmonic equations on graphs Liu, K.W

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:11:10.503145Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:10.085720Z digest=sha256:1b878327c6726222da46bc83e2e84b305ade82c4efe0eb5e9c3e7de38c31ef2a

Observation b999704f-eb3b-4a01-88ec-4b5476401635 · outbound

This paper cites McKenna, W.

Existence and convergence of solutions for nonlinear biharmonic equations on graphs McKenna, W

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:11:10.485081Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:10.096751Z digest=sha256:0d7eca354b2c3fe12c21340c92379615470a8c04178ee1a176081ec45ec9abcb

Observation 2f9cf7f7-d207-4e79-83ba-14cb7fd6cae4 · outbound

This paper cites Niu, Z.W.

Existence and convergence of solutions for nonlinear biharmonic equations on graphs Niu, Z.W

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:11:10.464349Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:10.103343Z digest=sha256:06fda7a600691ec3fdc171ed47011f73233bf08f287e2ab825dcfb4586e329b2

Observation 8c4ce47d-52f7-49dd-9b43-2f21b787ac69 · outbound

This paper cites Rabinowitz, On a class of nonlinear Schr¨ odinger equations, Z.

Existence and convergence of solutions for nonlinear biharmonic equations on graphs Rabinowitz, On a class of nonlinear Schr¨ odinger equations, Z

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:11:10.446088Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:10.117134Z digest=sha256:97b919a567e55454fdc3adebe0664e490ec97a3fe491be3ced79d1f757acb8ac

Observation 42e7514e-16ed-48e0-98f7-4990f45afc5d · outbound

This paper cites Sani, A biharmonic equation in R4 involving nonlinearities with critical exponential growth, Commun.

Existence and convergence of solutions for nonlinear biharmonic equations on graphs Sani, A biharmonic equation in R4 involving nonlinearities with critical exponential growth, Commun

Reference 26

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:11:10.422970Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:10.125687Z digest=sha256:82a6035ebb17fbd48b5b10a4228ad3ecefb13048f364a04465375486accc84ad

Observation 5b7f3091-f3fd-4dd4-9386-bc32120d6d30 · outbound

This paper cites Wang, Y.T.

Existence and convergence of solutions for nonlinear biharmonic equations on graphs Wang, Y.T

Reference 27

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:11:10.398546Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:10.130796Z digest=sha256:bb530cb6fbaae8d3ef7d842f47707dfb34f9ba0d3e9dd7a4c6d738a1dcc91965

Observation 044874d7-31a3-41ab-810e-442d9df8963d · outbound

This paper cites Wang, H.S.

Existence and convergence of solutions for nonlinear biharmonic equations on graphs Wang, H.S

Reference 28

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:11:10.375135Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:10.136777Z digest=sha256:2ad7246ca9b6b1db322d13cf5e6613e680a3798983d62e3ed0cb9caf508bd536

Observation 864ccf8b-fa5d-4bc4-81fc-157c7a5ebf14 · outbound

This paper cites Wojciechowski, Heat kernel and essential spectrum of infi nite graphs, Indiana Univ.

Existence and convergence of solutions for nonlinear biharmonic equations on graphs Wojciechowski, Heat kernel and essential spectrum of infi nite graphs, Indiana Univ

Reference 29

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:11:10.345755Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:10.142374Z digest=sha256:e73c0d0e4653a458498b10d47c93f3f84ad4cadab82cc2e045d807d0ab5e80e6

Observation 3095b70a-3765-4b4a-bdf3-16c525584c80 · outbound

This paper cites Yang, Existence of positive solutions to quasi-linear elliptic eq uations with exponential growth in the whole Euclidean space, J.

Existence and convergence of solutions for nonlinear biharmonic equations on graphs Yang, Existence of positive solutions to quasi-linear elliptic eq uations with exponential growth in the whole Euclidean space, J

Reference 30

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:11:10.322624Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:10.147028Z digest=sha256:9f50397099991c3474b0402a7f7552053fdc1455ca361f6a83e8fab87857736b

Observation 4e8c9835-2635-4686-b799-ca6c4dc6b47b · outbound

This paper cites Zhang, L.

Existence and convergence of solutions for nonlinear biharmonic equations on graphs Zhang, L

Reference 31

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:11:10.299935Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:10.152351Z digest=sha256:15aceea5d6df487640be4d5287ccad3b7e19f31de773931d1a5a2a33cef9acae

Observation f3d08e5d-0cf8-447d-a21b-6b66f0ce30c0 · outbound

This paper cites Zhang, Z.L.

Existence and convergence of solutions for nonlinear biharmonic equations on graphs Zhang, Z.L

Reference 32

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:11:10.279415Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:10.158168Z digest=sha256:4dce4c6d7eda33541d7a62082b19cf5b52ca55da3d0a52795fac03e7479346a9

Observation 877d2c8c-0e18-4168-b0fd-9f92c7eae9cf · outbound

This paper cites an unresolved cited work.

Existence and convergence of solutions for nonlinear biharmonic equations on graphs Unresolved cited work

Reference 33

Resolution
unresolved
raw_fallback, observed 2026-08-14T14:11:10.255216Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:11:10.163214Z digest=sha256:32cd75aa90fee1cc9ed9bcc05d495e7f2daa62611ec2deb8e4e8725e2c794937

Pith citing papers

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