Scholarlink

<p>In the paper, results on the existence of critical points in annular subsets of a cone are obtained with the additional goal of obtaining multiplicity results. Compared to other approaches in the literature based on the use of Krasnoselskii’s compression-extension theorem or topological index methods, our approach uses the Nehari manifold technique in a surprising combination with the cone version of Birkhoff-Kellogg’s invariant-direction theorem. This yields a simpler alternative to traditional methods involving deformation arguments or Ekeland’s variational principle. The new method is illustrated on a boundary value problem for <i>p</i>-Laplace equations, and we believe that it will be useful for proving the existence, localization, and multiplicity of solutions for other classes of problems with variational structure.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Critical point localization and multiplicity results in Banach spaces via Nehari manifold technique

  • 期刊论文

  • 发表日期：

    2026年1月3日

查看全文
  • Radu Precup,
  • Andrei Stan

摘要

In the paper, results on the existence of critical points in annular subsets of a cone are obtained with the additional goal of obtaining multiplicity results. Compared to other approaches in the literature based on the use of Krasnoselskii’s compression-extension theorem or topological index methods, our approach uses the Nehari manifold technique in a surprising combination with the cone version of Birkhoff-Kellogg’s invariant-direction theorem. This yields a simpler alternative to traditional methods involving deformation arguments or Ekeland’s variational principle. The new method is illustrated on a boundary value problem for p-Laplace equations, and we believe that it will be useful for proving the existence, localization, and multiplicity of solutions for other classes of problems with variational structure.