Description

• Title:
  Morse theory applied to a $T^{2}$-equivariant problem
• Creator:
  Vannella, Giuseppina
• Description:
  The following $T^2$-equivariant problem of periodic type is considered: $$ \cases u\in C^2({\mathbb R}^2,{\mathbb R}),\cr -\varepsilon\Delta u(x,y)+F^{\prime }(u(x,y))=0 & \text{in ${\mathbb R}^{2}$,}\cr u(x,y)=u(x+T,y)=u(x,y+S) &\text{for all $(x,y)\in {\mathbb R}^2$,}\cr \nabla u(x,y)=\nabla u(x+T,y)=\nabla u(x,y+S) &\text{for all $(x,y)\in {\mathbb R}^{2}$.} \endcases\tag{\text{P}} $$ Using a suitable version of Morse theory for equivariant problems, it is proved that an arbitrarily great number of orbits of solutions to (P) is founded, choosing $\varepsilon> 0$ suitably small. Each orbit is homeomorphic to $S^1$ or to $T^2$.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2001.03.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 17, No 1 (March 2001); 41 - 53;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2001.003/9954
• Subject:
  PDE;
  critical points;
  Morse theory;
  group actions;
  Primary 35J60;
  Secondary 58E40
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2001.003
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other