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arXiv · 2204.09506

Weak solvability of nonlinear elliptic equations involving variable exponents

A. Aberqi·J. Bennouna·O. Benslimane·M. A. Ragusa
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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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A. Aberqi, J. Bennouna, O. Benslimane, M. A. Ragusa. 2022-04-18. Weak solvability of nonlinear elliptic equations involving variable exponents. https://arxiv.org/abs/2204.09506

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