Description

• Title:
  Existence of solutions for the semilinear corner degenerate elliptic equations
• Creator:
  Kim, Jae-Myoung
• Description:
  In this paper, we are concerned with the following elliptic equations: \begin{equation*}\label{e:JG} \begin{cases} -\Delta_{\mathbb{M}}u = \lambda f &\textmd{in } z:= (r,x,t) \in \mathbb{M}_0,\\ u= 0 &\text{on } \partial\mathbb{M}. \end{cases} \end{equation*} Here, $\lambda > 0$ and $M=[0,1)\times X\times[0,1)$ as a local model of stretched corner-manifolds, that is, the manifolds with corner singularities with dimension $N=n+2\geq3$. Here $X$ is a closed compact submanifold of dimension $n$ embedded in the unit sphere of $\mathbb{R}^{n+1}$. We study the existence of nontrivial weak solutions for the semilinear corner degenerate elliptic equations without the Ambrosetti and Rabinowitz condition via the mountain pass theorem and fountain theorem.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2018 Topological Methods in Nonlinear Analysis
• Date:
  2018.11.03
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 52, No 2 (December 2018); 585 - 597;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2018.021/15958 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2018.021/15959
• Subject:
  Semilinear;
  corner;
  degenerate elliptic;
  35J20;
  58J05;
  35J75
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2018.021
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other