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<p>We consider a degenerate <i>p</i>-Laplacian equation, with a reaction that exhibits the competing effects of a parametric concave term and of a sign-changing convex perturbation. Using variational tools and critical groups, we prove an existence and multiplicity result which is global in the parameter. In the process, we also prove some general results of independent interest.</p>

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Exact multiplicity of positive solutions for degenerate concave-convex problems

  • 期刊论文

  • 发表日期：

    2026年6月17日

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  • Jiangfeng Han,
  • Zhenhai Liu,
  • Nikolaos S. Papageorgiou

摘要

We consider a degenerate p-Laplacian equation, with a reaction that exhibits the competing effects of a parametric concave term and of a sign-changing convex perturbation. Using variational tools and critical groups, we prove an existence and multiplicity result which is global in the parameter. In the process, we also prove some general results of independent interest.