Description

• Title:
  Sign-changing solutions for the boundary value problem involving the fractional $p$-Laplacian
• Creator:
  Wu, Pengcheng;
  Zhou, Yuying
• Description:
  In the paper, we consider the following boundary value problem involving the fractional $p$-Laplacian: \begin{equation} \tag{$\mathcal{P}$} \begin{cases} (-\triangle)_p^su(x)=f(x,u) &\text{in } \Omega,\\ u(x)=0 &\text{in } \mathbb{R}^N\setminus\Omega. \end{cases} \end{equation} where $\Omega$ is a bounded smooth domain in $\mathbb{R}^N$ with $N\geq 1$, $(-\Delta)_p^{s}$ is the fractional $p$-Laplacian with $s\in (0,1)$, $p\in(1,{N}/{s})$, $f(x, u)\colon \Omega\times\mathbb{R}\rightarrow\mathbb{R}$. Under the improved subcritical polynomial growth condition and other conditions, the existences of a least-energy sign-changing solution for the problem $(\mathcal{P})$ has been established.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2021 Topological Methods in Nonlinear Analysis
• Date:
  2021.05.25
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 57, No 2 (June 2021); 597 - 619;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2020.051/29011 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2020.051/29012
• Subject:
  Fractional $p$-Laplacian;
  sign-changing solutions;
  topology degree;
  deformation lemma;
  35J50;
  35J67;
  58J05
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2020.051
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other