Weak solvability of nonlinear elliptic equations involving variable exponents

2022/04/18 by A. Aberqi, J. Bennouna, Aberqi, A. +5
Mathematics · #Differential Equations and Boundary Problems #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2204.09506

openalex publication_date 2022/04/18 · openalex created_date 2022/10/07 · openalex updated_date 2026/07/28

Abstract

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 Ambrosetti-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.

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