Pith Number

pith:GVPGVZZP

pith:2026:GVPGVZZPO7ECU3TLS5RGSGBRO6

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Infinitely many multi-peaks solutions for a nonlinear Hartree system

Qihan He, Qingfang Wang

A three-component nonlinear Hartree system possesses infinitely many multi-peak solutions with mixed synchronization, segregation, and sign patterns.

arxiv:2605.13531 v1 · 2026-05-13 · math.AP

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Claims

C1strongest claim

Applying the Lyapunov-Schmidt reduction method, we prove the existence of infinitely many solutions to the system. Specifically, the solutions we obtain satisfy that some components are synchronized with each other but segregated from the others, and that some components are positive while others are sign-changing.

C2weakest assumption

The potentials V_i(x) are continuous bounded radial functions and the coupling constants β_ij allow the reduced functional to have the required critical points for the mixed synchronization-segregation and sign patterns; the abstract does not specify the precise range of β_ij or decay conditions on V_i.

C3one line summary

Infinitely many solutions exist for the 3-component Hartree system with some positive and some sign-changing components, constructed via Lyapunov-Schmidt reduction as the first such mixed-sign application.

References

54 extracted · 54 resolved · 0 Pith anchors

[1] Ackermann, On a periodic Schr¨ odinger equation with nonlocal superlinear part, Math 2004

[2] C. Alves, A. N´ obrega, M. Yang, Multi-bump solutions for Choquard equation with deepening potential well. Calc. Var. Partial Differ. Equ., 55 (2016), 28pp 2016

[3] A. Ambrosetti, G. Cerami, D. Ruiz, Solitons of linearly coupled systems of semilinear non-autonomous equations onR n, J. Funct. Anal., 254 (2008), 2816–2845 2008

[4] A. Ambrosetti, E. Colorado, Standing waves of some coupled nonlinear Schr¨ odinger equations. J. Lond. Math. Soc. (2), 75 (2007), 67–82 2007

[5] A. Ambrosetti, V. Fell, A. Malchiodi, Ground states of nonlinear Schr¨ odinger equa- tions with potentials vanishing at infinity. J. Eur. Math. Soc., 7 (2005), 117–144 2005

Receipt and verification

First computed	2026-05-18T02:44:24.219593Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

355e6ae72f77c82a6e6b976269183177a692109858b2b26dd572866ae35a04ff

Aliases

arxiv: 2605.13531 · arxiv_version: 2605.13531v1 · doi: 10.48550/arxiv.2605.13531 · pith_short_12: GVPGVZZPO7EC · pith_short_16: GVPGVZZPO7ECU3TL · pith_short_8: GVPGVZZP

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/GVPGVZZPO7ECU3TLS5RGSGBRO6 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 355e6ae72f77c82a6e6b976269183177a692109858b2b26dd572866ae35a04ff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ad188c383cc54b7b67a897d8f8012b1a70b9ba2fafa9bca8c2a6a10323d8ff5c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-05-13T13:42:42Z",
    "title_canon_sha256": "9636f2abb55e2cc3cd4723c73293d9ea8b9fe2947acf974086ed6a336debdfa1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13531",
    "kind": "arxiv",
    "version": 1
  }
}