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<p>In this paper, we use the Mountain pass theorem and the Fountain theorem to study the existence of solutions for the following <i>p</i>(<i>x</i>)-triharmonic equations: <Equation ID="Equa"> <MediaObject> <ImageObject Color="BlackWhite" FileRef="44198_2024_247_Article_Equa.gif" Format="GIF" Height="44" Rendition="HTML" Resolution="72" Type="Linedraw" Width="228" /> </MediaObject> <EquationSource Format="TEX">\(\begin{aligned} {\left\{ \begin{array}{ll} -\Delta _{p(x)}^{3} u=\lambda f(x,u), &amp; \hbox { in } \Omega,\\ u=\Delta u=\Delta ^{2}u=0, &amp; \hbox { on }\partial \Omega.\\ \end{array}\right. } \end{aligned}\)</EquationSource> </Equation></p>

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Existence of Solutions for p(x)-Triharmonic Problem with Navier Boundary Conditions

  • 期刊论文

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  • 发表日期：

    2025年2月18日

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  • Xiaohuan Zhao,
  • Qing Miao

摘要

In this paper, we use the Mountain pass theorem and the Fountain theorem to study the existence of solutions for the following p(x)-triharmonic equations: \(\begin{aligned} {\left\{ \begin{array}{ll} -\Delta _{p(x)}^{3} u=\lambda f(x,u), & \hbox { in } \Omega,\\ u=\Delta u=\Delta ^{2}u=0, & \hbox { on }\partial \Omega.\\ \end{array}\right. } \end{aligned}\)