Description

• Title:
  Multiplicity of positive solutions for fractional Laplacian equations involving critical nonlinearity
• Creator:
  Zhang, Jinguo;
  Liu, Xiaochun;
  Jiao, Hongying
• Description:
  In this paper, we consider the following problem involving fractional Laplacian operator \begin{equation*} (-\Delta)^{s} u=\lambda f(x)|u|^{q-2}u+|u|^{2^{*}_{s}-2}u\quad \text{in } \Omega,\qquad u=0\quad \text{on } \partial\Omega, \end{equation*} where $\Omega$ is a smooth bounded domain in $\mathbb{R}^{N}$, $0< s< 1$, $2^*_{s}={2N}/({N-2s})$, and $(-\Delta)^{s}$ is the fractional Laplacian. We will prove that there exists $\lambda_{*}> 0$ such that the problem has at least two positive solutions for each $\lambda\in (0,\lambda_{*})$. In addition, the concentration behavior of the solutions are investigated.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2019 Topological Methods in Nonlinear Analysis
• Date:
  2019.02.16
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 53, No 1 (March 2019); 151 - 182;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2018.043/16835 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2018.043/16836
• Subject:
  Fractional Laplacian equation;
  critical Sobolev exponent;
  variational methods;
  35J60;
  47J30
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2018.043
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other