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Abstract <p>We study superlinear fractional <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11957_2025_7226_Article_IEq5.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(p\)</EquationSource> <!--ContMath2460153Pei-m5--> </InlineEquation>-Laplacian equations in <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11957_2025_7226_Article_IEq6.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb{R}^{N}\)</EquationSource> <!--ContMath2460153Pei-m6--> </InlineEquation> with periodic potential. When nonlinearities satisfy critical exponential growth (subcritical polynomial growth or subcritical exponential growth) at <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11957_2025_7226_Article_IEq7.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(\infty\)</EquationSource> <!--ContMath2460153Pei-m7--> </InlineEquation> without satisfying the classical Ambrosetti–Rabinowitz (AR) condition, by using the mountain pass theorem and Nehari manifold methods combined with the fractional Moser–Trudinger inequality, several existence results for ground state solutions are established.</p>

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Existence of Ground State Solutions for Fractional \(\boldsymbol{p}\)-Laplacian Equations in \(\boldsymbol{\mathbb{R}^{N}}\) Involving Exponential Growth

  • 期刊论文

  • 发表日期：

    2025年6月27日

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  • R. Pei,
  • C. Ma

摘要

Abstract

We study superlinear fractional \(p\) -Laplacian equations in \(\mathbb{R}^{N}\) with periodic potential. When nonlinearities satisfy critical exponential growth (subcritical polynomial growth or subcritical exponential growth) at \(\infty\) without satisfying the classical Ambrosetti–Rabinowitz (AR) condition, by using the mountain pass theorem and Nehari manifold methods combined with the fractional Moser–Trudinger inequality, several existence results for ground state solutions are established.