Generalized critical Kirchhoff-type potential systems with Neumann Boundary conditions

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 multipli...

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Published inApplicable analysis Vol. 101; no. 11; pp. 3958 - 3988
Main Authors Chems Eddine, Nabil, Ragusa, Maria Alessandra
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 24.07.2022
Taylor & Francis Ltd
Subjects
Boundary conditions
concentration-compactness principle
critical points theory
critical Sobolev exponents
generalized Capillary operator
Kirchhoff-type problems
Laplacian
mountain pass theorem
Neumann Boundary conditions
p-Laplcian
Palais-Smale condition
Variable exponent spaces
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ISSN0003-6811
1563-504X
DOI10.1080/00036811.2022.2057305

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Summary: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 and the mountain pass theorem without the Palais-Smale condition.
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ISSN:0003-6811
1563-504X
DOI:10.1080/00036811.2022.2057305