Description

• Title:
  Positive solutions of Kirchhoff-Hénon type elliptic equations with critical Sobolev growth
• Creator:
  Takahashi, Kazune
• Description:
  We investigate the following Kirchhoff-Hénon type equation involving the critical Sobolev exponent with Dirichlet boundary condition: \[ - \bigg( a + b \bigg( \int_\Omega \lvert Du \rvert^2 dx \bigg)^{(p-2)/2} \bigg) \Delta u = \Psi u^{q-1} + \lvert x \rvert^\alpha u^{2^* - 1} \] in $\Omega$ included in a unit ball under several conditions. Here, $a, b \geq 0$, $a + b > 0$, $2 < p < q < 2^*$ and $\Psi \in L^\infty(\Omega) \setminus \{ 0 \}$ is a given non-negative function with several conditions. We show that, if either $N = 3$ with $4 < q < 2^* = 6$ or $N \geq 4$, there exists a positive solution for small $\alpha \geq 0$. Our methods includes the mountain pass theorem and the Talenti function.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2020 Topological Methods in Nonlinear Analysis
• Date:
  2020.03.04
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 55, No 1 (March 2020); 317 - 341;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2019.096/25008 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2019.096/25009
• Subject:
  Critical Sobolev exponent;
  Kirchhoff equation;
  Henon equation;
  mountain pass theorem;
  Talenti function;
  35J20;
  35J60;
  35J61;
  35J91
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2019.096
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other