Nonlinear Elliptic Equations With Variable Exponents Satisfying Cerami\n Condition

2021/04/29 by Omar Benslimane, Benslimane, Omar, Ahmed Aberqi +3
Mathematics · #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2104.14689

openalex publication_date 2021/04/29 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

We are concerned with the study of the existence and multiplicity of\nsolutions for Dirichlet boundary value problems involving the (p(x),\nq(x))-equation and the nonlinearity is superlinear but does not satisfy the\nusual Ambrossetti-Rabinowitz condition in the framework of Sobolev spaces with\nvariable exponents in Complete manifolds. The main results are established by\nmeans of the mountain pass theorem and Fountain theorem with Cerami condition.\nMoreover, we are giving an example of a (p(x), q(x)) equation that verifies all\nour demonstrated results.\n

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