WEAK SOLVABILITY OF NONLINEAR ELLIPTIC EQUATIONS INVOLVING VARIABLE EXPONENTS

被引：7

作者：

Aberqi, Ahmed ^{[1
]}

Bennouna, Jaouad ^{[2
]}

Benslimane, Omar ^{[2
]}

Ragusa, Maria Alessandra ^{[3
,4
]}

机构：

[1] Sidi Mohamed Ben Abdellah Univ, Lab LAMA, Natl Sch Appl Sci, Fes, Morocco

[2] Sidi Mohamed Ben Abdellah Univ, Lab LAMA, Dept Math, Fac Sci Dhar El Mahraz, BP 1796 Atlas Fez, Fez, France

[3] Univ Catania, Dipartimento Matemat & Informat, Catania, Italy

[4] RUDN Univ, 6 Miklukho Maklay St, Moscow 117198, Russia

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2023年 / 16卷 / 06期

关键词：

Laplacian; elliptic equation; non-trivial solutions; Cerami sequences; Sobolev-Orlicz Riemannian manifold with variable exponents; EXISTENCE; UNIQUENESS;

D O I：

10.3934/dcdss.2022105

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We are concerned with the study of the existence and multiplicity of solutions for Dirichlet boundary value problems, involving the (p(m); q(m))-equation and the nonlinearity is superlinear but does not fulfil the Ambrossetti-Rabinowitz condition in the framework of Sobolev spaces with variable exponents in a complete manifold. The main results are proved using the mountain pass theorem and Fountain theorem with Cerami sequences. Moreover, an example of a (p(m); q(m)) equation that highlights the applicability of our theoretical results is also provided.

引用

页码：1142 / 1157

页数：16

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