Description

• Title:
  The effect of topology on the number of positive solutions of elliptic equation involving Hardy-Littlewood-Sobolev critical exponent
• Creator:
  Goel, Divya
• Description:
  In this article we are concerned with the following Choquard equation \begin{alignat*}2 -\Delta u &= \la|u|^{q-2}u +\bigg(\int_{\Omega}\frac{|u(y)|^{2^*_{\mu}}}{|x-y|^{\mu}}dy\bigg)|u|^{2^*_{\mu}-2}u,\quad u> 0, &\quad& \text{in }\Omega,\\ u& = 0 &\quad& \text{on } \partial \Omega , \end{alignat*} where $\Omega$ is an open bounded set with continuous boundary in $\mathbb{R}^N( N\geq 3)$, $2^*_{\mu}=({2N-\mu})/({N-2})$ and $q \in [2,2^*)$ where $2^*={2N}/({N-2})$. Using Lusternik-Schnirelman theory, we associate the number of positive solutions of the above problem with the topology of $\Omega$. Indeed, we prove that if $\la< \la_1$, then problem has $\text{cat}_{\Omega}(\Omega)$ positive solutions whenever $q \in [2,2^*)$ and $N> 3 $ or $4< q< 6 $ and $N=3$.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2019 Topological Methods in Nonlinear Analysis
• Date:
  2019.11.09
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 54, No 2 (December 2019); 751 - 771;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2019.068/23630 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2019.068/23631
• Subject:
  Choquard equation;
  critical exponent;
  Lusternik-Schnirelman theory;
  49J35;
  35A15;
  35J60
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2019.068
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other