Bifurcation from infinity with applications to reaction-diffusion systems

Chihiro Aida, Chao Nien Chen, Kousuke Kuto, Hirokazu Ninomiya

研究成果: Article

抄録

The bifurcation method is one of powerful tools to study the existence of a continuous branch of solutions. However without further analysis, the local theory only ensures the existence of solutions within a small neighborhood of bifurcation point. In this paper we extend the theory of bifurcation from infinity, initiated by Rabinowitz [11] and Stuart [13], to find solutions of elliptic partial differential equations with large amplitude. For the applications to the reaction-diffusion systems, we are able to relax the conditions to obtain the bifurcation from infinity for the following nonlinear terms; (i) nonlinear terms satisfying conditions similar to [11] (all directions), (ii) nonlinear terms satisfying similar conditions only on the strip domain along the direction determined by the eigenfunction, (iii) p-homogeneous nonlinear terms with degenerate conditions.

本文言語English
ページ(範囲)3031-3055
ページ数25
ジャーナルDiscrete and Continuous Dynamical Systems- Series A
40
6
DOI
出版ステータスPublished - 2020

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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