Scholarlink

<p>In this paper, we present multiplicity results related to mixed boundary value problem for a complete Sturm–Liouville equation. Specifically, we utilize a consequence of Bonanno’s local minimum theorem to establish the existence of one solution under certain algebraic conditions on the nonlinear term. In addition, we demonstrate that two solutions can be obtained under algebraic conditions while adhering to the classical Ambrosetti–Rabinowitz (AR) condition for the nonlinear term. Moreover, by applying two critical point theorems, one by Averna and Bonanno and another by Bonanno, we ensure the existence of two or three solutions for our problem in a particular scenario. We also provide an illustrative example to highlight our results.</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 Approaches for the Existence of Multiple Solutions of a Mixed Boundary Value Problem for a Complete Sturm–Liouville Equation

  • 期刊论文

  • 发表日期：

    2025年11月14日

查看全文
  • Massimiliano Ferrara,
  • Shapour Heidarkhani,
  • Shahin Moradi,
  • Donal O’Regan

摘要

In this paper, we present multiplicity results related to mixed boundary value problem for a complete Sturm–Liouville equation. Specifically, we utilize a consequence of Bonanno’s local minimum theorem to establish the existence of one solution under certain algebraic conditions on the nonlinear term. In addition, we demonstrate that two solutions can be obtained under algebraic conditions while adhering to the classical Ambrosetti–Rabinowitz (AR) condition for the nonlinear term. Moreover, by applying two critical point theorems, one by Averna and Bonanno and another by Bonanno, we ensure the existence of two or three solutions for our problem in a particular scenario. We also provide an illustrative example to highlight our results.