Description

• Title:
  Positive solutions of singularly perturbed nonlinear elliptic problem on Riemannian manifolds with boundary
• Creator:
  Ghimenti, Marco;
  Micheletti, Anna Maria
• Description:
  Let $(M,g)$ be a smooth connected compact Riemannian manifold of finite dimension $n\geq 2$\ with a smooth boundary $\partial M$. We consider the problem $$ \cases -\varepsilon ^{2}\Delta _{g}u+u=|u|^{p-2}u,\quad u> 0 &\text{ on }M,\\ \displaystyle \frac{\partial u}{\partial \nu }=0 & \text{on }\partial M, \endcases $$ where $\nu $ is an exterior normal to $\partial M$. The number of solutions of this problem depends on the topological properties of the manifold. In particular we consider the Lusternik Schnirelmann category of the boundary.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2010.04.23
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 35, No 2 (June 2010); 319 - 337;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2010.019/8446
• Subject:
  Remannian manifold with boundary;
  semiclassical limit;
  Lusternik-Schnirelmann category;
  58J23;
  58E30
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2010.019
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other