Existence and multiplicity of solutions involving the $ p(x) $-Laplacian equations: On the effect of two nonlocal terms
Mohamed Karim Hamdani, Lamine Mbarki, Mostafa Allaoui, Omar Darhouche, Dušan Repovš
Abstract
<p style='text-indent:20px;'>We study a class of <inline-formula><tex-math id="M2">\begin{document}$ p(x) $\end{document}</tex-math></inline-formula>-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.
Topics & Concepts
Mountain pass theoremMathematicsMultiplicity (mathematics)Mountain passClass (philosophy)Nonlinear systemVariational principlePure mathematicsMathematical analysisApplied mathematicsPhysicsComputer scienceQuantum mechanicsArtificial intelligenceNonlinear Partial Differential EquationsAdvanced Mathematical Modeling in EngineeringNonlinear Differential Equations Analysis