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<p>We discuss, by mountain pass lemma, the existence of nontrivial weak solutions for a class of triharmonic equations with two kinds of boundary conditions: Navier boundary conditions and Dirichlet boundary conditions. Infinitely many nontrivial weak solutions are also analyzed using critical point theory for even functionals. In addition, using the theory of strongly monotone operator, the uniqueness and limiting behavior of weak solution are also considered.</p>

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Nontrivial Solutions for Triharmonic Equations: Existence, Uniqueness, Multiplicity and Limiting Behavior

  • 期刊论文

  • 发表日期：

    2026年3月27日

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  • Meiqiang Feng,
  • Yichen Lu

摘要

We discuss, by mountain pass lemma, the existence of nontrivial weak solutions for a class of triharmonic equations with two kinds of boundary conditions: Navier boundary conditions and Dirichlet boundary conditions. Infinitely many nontrivial weak solutions are also analyzed using critical point theory for even functionals. In addition, using the theory of strongly monotone operator, the uniqueness and limiting behavior of weak solution are also considered.