On the Existence of Disjoint Infinite Solution Sets for a Critical Hardy-Sobolev-Maz’ya Equation

Paper Details

Authors: Echarghaoui R.; El Mansour M.; Masmodi M.

DOI: 10.28924/2291-8639-24-2026-197

Journal: International Journal of Analysis and Applications

Year: 2026

Publisher: Etamaths Publishing

Document Type: Article

Open Access: All Open Access; Gold Open Access

Cited by: 0

Abstract

In this work, we study the following Hardy–Sobolev–Maz’ya equation involving critical growth: (Formula presented) where Ω ⊂ RN is a bounded domain containing a point x0 = (0, z0) ∈ Rk × RN−k, with 2 ≤ k < N, x = (y, z), 0 ≤ s < 2, and (Formula presented). We assume (Formula presented) for k > 2, and λ = 0 when k = 2, with parameters satisfying 1 < q < 2, µ > 0, and (Formula presented). Using an approximating argument, local Pohozaev-type identities, and variational methods, including the Fountain Theorem and its dual version, we establish the existence of two disjoint and infinite sets of solutions under these assumptions. © 2026 the author(s).

Keywords

concave-convex nonlinearities; fountain theorem; Hardy-Sobolev-Maz’ya equation; infinitely many solutions

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