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<p>This manuscript is concerning to prove the existence of at least one weak solution using the topological degree theory for a Ni–Serrin type equation arising from capillary phenomena. We also derive two multiplicity results for non-trivial weak solutions of this equation. First, using a symmetric version of the mountain pass theorem, we demonstrate that our problem has an unbounded sequence of weak solutions. Second, we prove a multiplicity result using Lusternik–Schnirelmann category theory.</p>

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Existence and multiplicity of weak solutions for a Ni–Serrin type equation

  • 期刊论文

  • 发表日期：

    2026年3月6日

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  • M. Ait Hammou,
  • L. Mbarki,
  • D. Choudhuri

摘要

This manuscript is concerning to prove the existence of at least one weak solution using the topological degree theory for a Ni–Serrin type equation arising from capillary phenomena. We also derive two multiplicity results for non-trivial weak solutions of this equation. First, using a symmetric version of the mountain pass theorem, we demonstrate that our problem has an unbounded sequence of weak solutions. Second, we prove a multiplicity result using Lusternik–Schnirelmann category theory.