Acta mathematica scientia,Series A ›› 2026, Vol. 46 ›› Issue (4): 1393-1405.

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Existence of Multi-peak Solutions to the Neumann Problem for a $p$-Laplace Equation

Xujia Wang(), Xinyue Zhang*()   

  1. Institute for Theoretical Sciences, Westlake University, Hangzhou 310030
  • Received:2025-12-23 Revised:2026-03-19 Online:2026-08-26 Published:2026-06-10
  • Contact: Xinyue Zhang E-mail:wangxujia@westlake.edu.cn;zhangxinyue@westlake.edu.cn

Abstract:

In this paper, by applying a new minimax principle, we study the existence of multi-peak solutions to the Neumann problem for the $p$-Laplace equation

$-\varepsilon^p \Delta_p u = f(u) - u^{p-1} \ \ x\in \Omega,$

where $\Omega$ is a bounded smooth domain in $\mathbb{R}^n$, $1<p<n$, $\varepsilon>0$ is a small parameter, and $f$ is a superlinear subcritical nonlinearity.

Key words: Neumann problem, multi-peak solution, $p$-Laplace equation

CLC Number: 

  • O175
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