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<p>In this work, we study the existence and multiplicity of nontrivial weak solutions for a <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11784_2025_1237_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="31" /> </InlineMediaObject> <EquationSource Format="TEX">\(r(\zeta )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>r</mi> <mo stretchy="false">(</mo> <mi>ζ</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-Laplacian-like problem arising from capillary phenomena with effect of two nonlocal terms and without the Ambrosetti–Rabinowitz condition, by applying of the Mountain Pass Theorem, the Symmetric Mountain Pass Theorem, and Fountain Theorem, in the context of variable exponents of Sobolev spaces on compact Riemannian manifolds.</p>

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Nonlinear \(r(\zeta )\)-Laplacian-like problem with two nonlocal terms and without Ambrosetti–Rabinowitz condition on compact Riemannian manifolds

  • 期刊论文

  • 发表日期：

    2025年9月3日

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  • Guangwang Su,
  • Hind Bouaam,
  • Mohamed El Ouaarabi,
  • Said Melliani,
  • Van Thien Nguyen

摘要

In this work, we study the existence and multiplicity of nontrivial weak solutions for a \(r(\zeta )\) r ( ζ ) -Laplacian-like problem arising from capillary phenomena with effect of two nonlocal terms and without the Ambrosetti–Rabinowitz condition, by applying of the Mountain Pass Theorem, the Symmetric Mountain Pass Theorem, and Fountain Theorem, in the context of variable exponents of Sobolev spaces on compact Riemannian manifolds.