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<p>In this paper, we study a Kirchhoff-type problem driven by a multi-phase operator with three variable exponents. Such problem has a right-hand side consisting of a Carathéodory perturbation which is defined only locally as well as the Kirchhoff term. Using a generalized version of the symmetric mountain pass theorem along with recent a priori upper bounds for multi-phase problems, we get whole a sequence of nontrivial solutions for our problem converging to zero in the appropriate Musielak-Orlicz Sobolev space and in <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10440_2025_711_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="49" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mi mathvariant="normal">∞</mi> </msup> <mo stretchy="false">(</mo> <mi mathvariant="normal">Ω</mi> <mo stretchy="false">)</mo> </math></EquationSource> <EquationSource Format="TEX">$L^{\infty }(\Omega )$</EquationSource> </InlineEquation>.</p>

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Multiplicity of Solutions for a Kirchhoff Multi-Phase Problem with Variable Exponents

  • 期刊论文

  • 发表日期：

    2025年1月24日

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  • Francesca Vetro

摘要

In this paper, we study a Kirchhoff-type problem driven by a multi-phase operator with three variable exponents. Such problem has a right-hand side consisting of a Carathéodory perturbation which is defined only locally as well as the Kirchhoff term. Using a generalized version of the symmetric mountain pass theorem along with recent a priori upper bounds for multi-phase problems, we get whole a sequence of nontrivial solutions for our problem converging to zero in the appropriate Musielak-Orlicz Sobolev space and in L ∞ ( Ω ) $L^{\infty }(\Omega )$ .