Multiple Solutions for Problems Involving p(x)-Laplacian and p(x)-Biharmonic Operators

被引：0

作者：

Sahbani, Abdelhakim ^{[1
]}

Ghanmi, Abdeljabbar ^{[1
]}

Chammem, Rym ^{[1
]}

机构：

[1] Univ Tunis Manar, Fac Sci, Math Dept, Tunis 2092, Tunisia

来源：

JOURNAL OF MATHEMATICAL PHYSICS ANALYSIS GEOMETRY | 2024年 / 20卷 / 02期

关键词：

p(x)-biharmonic operator; p(x)-Laplacian; symmetric moun- tain pass theorem; generalized Sobolev space; NONTRIVIAL SOLUTIONS; VARIABLE EXPONENT; FUNCTIONALS; EXISTENCE;

D O I：

10.15407/mag20.02.235

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider the following p(x)-biharmonic problem with Hardy nonlinearity: Delta 2p ( x )u -Delta p ( x )u = lambda(| u|p ( x ) - 2u)/delta( x)2p ( x )+ f( x , u ) in Omega, u= 0 on partial derivative ohm, |delu|p (( x ) - 2)partial derivative u/partial derivative n= g( x , u ) on partial derivative ohm, where Omega c R (N) (N > 3), Delta (p(x)) is the p(x)-Laplacian and Delta (2)(p(x)) is the p(x)biharmonic operator. More precisely, under some appropriate conditions on the nonlinearities f and g, we combine the variational methods with the theory of the generalized Lebesgue and Sobolev spaces to prove the existence and the multiplicity of solutions.

引用

页码：235 / 249

页数：15

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