Existence and multiplicity of solutions involving the \(p(x)\)-Laplacian equations: On the effect of two nonlocal terms

We study a class of \(p(x)\)-Kirchhoff problems which is seldom studied because the nonlinearity has nonstandard growth and contains a bi-nonlocal term. Based on variational methods, especially the Mountain pass theorem and Ekeland's variational principle, we obtain the existence of two nontriv...

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Bibliographic Details
Published inarXiv.org
Main Authors Hamdani, M K, Mbarki, L, Allaoui, M, Darhouche, O, Repovš, D D
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 16.06.2022
Subjects
Existence theorems
Laplace equation
Mountains
Variational methods
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Summary:We study a class of \(p(x)\)-Kirchhoff problems which is seldom studied because the nonlinearity has nonstandard growth and contains a bi-nonlocal term. Based on variational methods, especially the Mountain pass theorem and Ekeland's variational principle, we obtain the existence of two nontrivial solutions for the problem under certain assumptions. We also apply the Symmetric mountain pass theorem and Clarke's theorem to establish the existence of infinitely many solutions. Our results generalize and extend several existing results.
ISSN:2331-8422
DOI:10.48550/arxiv.2206.08066