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

被引：7

作者：

Chems Eddine, Nabil ^{[1
]}

Repovs, Dusan D. ^{[2
,3
,4
]}

机构：

[1] Mohammed V Univ, Fac Sci, Dept Math, Lab Math Anal & Applicat, POB 1014, Rabat, Morocco

[2] Univ Ljubljana, Fac Educ, Ljubljana, Slovenia

[3] Univ Ljubljana, Fac Math & Phys, Ljubljana, Slovenia

[4] Inst Math Phys & Mech, Ljubljana, Slovenia

来源：

BOUNDARY VALUE PROBLEMS | 2023年 / 2023卷 / 01期

关键词：

Kirchhoff-type problems; Neumann boundary conditions; p(x )-Laplacian operator; Generalized capillary operator; Sobolev spaces with variable exponent; Critical Sobolev exponents; Concentration-compactness principle; Critical point theory; Truncation technique; MULTIPLE SOLUTIONS; VARIABLE EXPONENT; P(X)-LAPLACIAN EQUATIONS; ELLIPTIC-EQUATIONS; POSITIVE SOLUTIONS; SPACES; EXISTENCE; GROWTH;

D O I：

10.1186/s13661-023-01705-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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.

引用

页数：33

共 51 条

[1] EXISTENCE OF SOLUTIONS FOR A CLASS OF p(x)-LAPLACIAN EQUATIONS INVOLVING A CONCAVE-CONVEX NONLINEARITY WITH CRITICAL GROWTH IN RN [J].