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  and Stuart , 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  (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.
|Number of pages||25|
|Journal||Discrete and Continuous Dynamical Systems- Series A|
|Publication status||Published - 1 Jan 2020|
- Bifurcation from infinity
- Reaction-diffusion systems