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Open Access Research Article

Infinitely many solutions for a Neumann elliptic system with critical exponents and hardy potentials

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pp. 1–23Online FirstMarch 2026DOI: 10.47974/JIM-2331XML
Received:
02 Jun 2025
Published Online:
30 Mar 2026
Article type:
Research Article
Language:
EN
Article no.:
JIM-2331
Pages:
1–23

Abstract

Using concentration estimates along with the Fountain Theorem and its dual form, we establish the existence of two infinite and disjoint sets of solutions for the following Neumann elliptic system involving critical Sobolev exponents, a Hardy potential, and a concave-convex nonlinearity: where Ω ⊂ RN is a smooth bounded domain containing the origin, with N ≥ 7, α1 + β1 = 2*, β ̅ = ((N-2)2/4,  β =  β ∈ [0, β ̅  – 4), 2* – √(1-β/β ̅ ) <α2 + β2 < 2, and 2* := 2N/(N-2) denotes the critical Sobolev exponent.

Keywords

Subject Classifications

35J6035B33

References

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