Description

• Title:
  Multiplicity results for nonlocal fractional $p$-Kirchhoff equations via Morse theory
• Creator:
  Zhang, Binlin;
  Bisci, Giovanni Molica;
  Xiang, Mingqi
• Description:
  In this paper, we apply Morse theory and local linking to study the existence of nontrivial solutions for Kirchhoff type equations involving the nonlocal fractional $p$-Laplacian with homogeneous Dirichlet boundary conditions: \begin{align*} \begin{cases} \!\bigg[M\bigg(\displaystyle\iint_{\mathbb{R}^{2N}}\!\frac{|u(x)-u(y)|^p}{|x-y|^{N+ps}}dxdy\bigg)\bigg]^{p-1} \!(-\Delta)_p^su(x)=f(x,u)&\mbox{in }\Omega,\\ u=0&\mbox{in } \mathbb{R}^{N}\setminus\Omega, \end{cases} \end{align*} where $\Omega$ is a smooth bounded domain of $\mathbb{R}^N$, $(-\Delta)_p^s$ is the fractional $p$-Laplace operator with $0< s< 1< p< \infty$ with $sp< N$, $M \colon \mathbb{R}^{+}_{0}\rightarrow \mathbb{R}^{+}$ is a continuous and positive function not necessarily satisfying the increasing condition and $f$ is a Carathéodory function satisfying some extra assumptions.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2016.11.23
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 49, No 2 (June 2017); 445 - 461;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2016.081/10410 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2016.081/10411
• Subject:
  Fractional $p$-Laplacian;
  Kirchhoff type equations;
  Morse theory;
  local linking;
  35R11;
  35A15;
  35J60;
  58E05
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2016.081
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other