The Neumann problem for a class of generalized Kirchhoff-type potential systems

被引：0
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作者：
Nabil Chems Eddine
Dušan D. Repovš
机构：
[1] Mohammed V University,Laboratory of Mathematical Analysis and Applications, Department of Mathematics, Faculty of Sciences
[2] University of Ljubljana,Faculty of Education
[3] University of Ljubljana,Faculty of Mathematics and Physics
[4] Institute of Mathematics,undefined
[5] Physics and Mechanics,undefined
来源：
Boundary Value Problems | / 2023卷
关键词：
Kirchhoff-type problems; Neumann boundary conditions; -Laplacian operator; Generalized capillary operator; Sobolev spaces with variable exponent; Critical Sobolev exponents; Concentration–compactness principle; Critical point theory; Truncation technique; 35B33; 35D30; 35J50; 35J60; 46E35;
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学科分类号：
摘要：
In this paper, we are concerned with the Neumann problem for a class of quasilinear stationary Kirchhoff-type potential systems, which involves general variable exponents elliptic operators with critical growth and real positive parameter. We show that the problem has at least one solution, which converges to zero in the norm of the space as the real positive parameter tends to infinity, via combining the truncation technique, variational method, and the concentration–compactness principle for variable exponent under suitable assumptions on the nonlinearities.
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