Description

• Title:
  Index bundle, Leray-Schauder reduction and bifurcation of solutions of nonlinear elliptic boundary value problems
• Creator:
  Pejsachowicz, Jacobo
• Description:
  We show that a family $F_p;\ p\in P$ of nonlinear elliptic boundary value problems of index $0$ parametrized by a compact manifold admits a reduction to a family of compact vector fields parametrized by $P$ if and only if its index bundle $\text{\rm Ind}F$ vanishes. Our second conclusion is that, in the presence of bounds for the solutions of the boundary value problem, the non vanishing of the image of the index bundle under generalized $J$-homomorphism produces restrictions on the possible values of the degree of $F_p$. The most striking manifestation of this arises when the first Stiefel-Whitney class of the index bundle is nontrivial. In this case, the degree of $F_p$ must vanish! From this we obtain a number of corollaries about bifurcation from infinity for solutions of nonlinear elliptic boundary value problems.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2001.12.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 18, No 2 (December 2001); 243 - 267;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2001.033/9924
• Subject:
  Bifurcation;
  index bundle;
  fredholm operators;
  Leray-Schauder degree;
  nonlinear elliptic BVP;
  54H25;
  47H10;
  49J40;
  52A07;
  49J35
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2001.033
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other