Description

• Title:
  Positive radial solutions of the Dirichlet problem for the Minkowski-curvature equation in a ball
• Creator:
  Coelho, Isabel;
  Corsato, Chiara;
  Rivetti, Sabrina
• Description:
  We study the existence and multiplicity of positive radial solutions of the Dirichlet problem for the Minkowski-curvature equation $$ \cases \displaystyle -\text{\rm div}\bigg( \frac{\nabla v} {\sqrt{1 - |\nabla v|^2}}\bigg)= f(|x|,v) &\quad \text{in } B_R, \\ \displaystyle v=0 & \quad \text{on } \partial B_R, \endcases $$ < p> where $B_R$ is a ball in $\mathbb{R}^N$ ($N\ge 2$). According to the behaviour of $f=f(r,s)$ near $s=0$, we prove the existence of either one, two or three positive solutions. All results are obtained by reduction to an equivalent non-singular one-dimensional problem, to which variational methods can be applied in a standard way.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2016.04.12
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 44, No 1 (September 2014); 23 - 39;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2014.034/8148
• Subject:
  Quasilinear elliptic differential equation;
  Minkowski-curvature;
  Dirichlet boundary condition;
  radial solution;
  positive solution;
  existence;
  multiplicity;
  variational methods;
  35J25;
  35J60;
  35J62;
  35J20;
  35J93;
  47J30
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2014.034
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other