Description

• Title:
  On a power-type coupled system of Monge-Ampère equations
• Creator:
  Qi, Zexin;
  Zhang, Zhitao
• Description:
  We study an elliptic system coupled by Monge--Amp\`{e}re equations:$$\begin{cases}      \det D^{2}u_{1}={(-u_{2})}^\alpha & \hbox{in  $\Omega,$} \\      \det D^{2}u_{2}={(-u_{1})}^\beta & \hbox{in $\Omega,$} \\      u_{1}<0,\ u_{2}<0& \hbox{in  $\Omega,$}\\     u_{1}=u_{2}=0 & \hbox{on $ \partial \Omega,$}   \end{cases}$$%here $\Omega$~is a smooth, bounded and strictly convex domainin~$\mathbb{R}^{N}$, $N\geq2$, $\alpha >0$, $\beta >0$. When $\Omega$ isthe unit ball in $\mathbb{R}^{N}$, we use index theory of fixedpoints for completely continuous operators to get existence, uniqueness results and nonexistence of radial convex solutions undersome corresponding assumptions on $\alpha$, $\beta$. When $\alpha>0$,$\beta>0$ and $\alpha\beta=N^2$  we also study a~corresponding eigenvalue problem in more general domains.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2015 Topological Methods in Nonlinear Analysis
• Date:
  2015.12.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 46, No 2 (December 2015); 717 - 730;
  1230-3429
• Format:
  application/pdf
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2015.064/7261 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2015.064/7298
• Subject:
  System of Monge-Ampère equations;
  cone;
  fixed point index;
  generalized Krein-Rutman theorem;
  35J60;
  35J65;
  35J96
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2015.064
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other