Scholarlink

<p>We study a nonlinear eigenvalue problem driven by a general nonhomogeneous differential operator, involving a reaction term that is singular at <i>x</i> = 0 and becomes superlinear as <i>x</i> → +∞. Unlike the usual case in the literature, the singular term and the perturbation are not decoupled. By using variational methods in combination with truncation and comparison techniques, we establish a global existence and multiplicity theorem with respect to the parameter (eigenvalue) <i>λ</i> &gt; 0. Additionally, we demonstrate the existence of a minimal positive solution <i>u*</i><sub><i>λ</i></sub> and investigate the continuity and monotonicity properties of the map <i>λ</i> → <i>u*</i><sub><i>λ</i></sub>.</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

Nonlinear singular eigenvalue problems

  • 期刊论文

  • 发表日期：

    2026年5月9日

查看全文
  • Nikolaos S. Papageorgiou,
  • Zijia Peng

摘要

We study a nonlinear eigenvalue problem driven by a general nonhomogeneous differential operator, involving a reaction term that is singular at x = 0 and becomes superlinear as x → +∞. Unlike the usual case in the literature, the singular term and the perturbation are not decoupled. By using variational methods in combination with truncation and comparison techniques, we establish a global existence and multiplicity theorem with respect to the parameter (eigenvalue) λ > 0. Additionally, we demonstrate the existence of a minimal positive solution u*λ and investigate the continuity and monotonicity properties of the map λ → u*λ.