Generalized critical Kirchhoff-type potential systems With Neumann Boundary conditions

2022/03/21 by Nabil Chems Eddine, Eddine, Nabil Chems, Maria Alessandra Ragusa +1
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.AP #math.MP

paper · pdf · doi:10.48550/arxiv.2203.11942

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arxiv created 2022/03/21 · arxiv updated 2022/03/24

Abstract

In this paper, we consider a class of quasilinear stationary Kirchhoff type potential systems with Neumann Boundary conditions, which involves a general variable exponent elliptic operator with critical growth. Under some suitable conditions on the nonlinearities, we establish existence and multiplicity of solutions for the problem by using the concentration-compactness principle of Lions for variable exponents found in [5, 7] and the Mountain Pass Theorem without the Palais-Smale condition given in [43].

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