Generic properties of the Rabinowitz unbounded continuum

Abstract

In this article, we prove that, generically in the sense of domain variations, any solution to a nonlinear eigenvalue problem is either nondegenerate or the Crandall-Rabinowitz transversality condition that is satisfied. We then deduce that, generically, the unbounded Rabinowitz continuum of solutions is a simple analytic curve. The global bifurcation diagram resembles the classic model case of the Gel’fand problem in two dimensions.

Keywords

• rabinowitz continuum
• bifurcation analysis
• generic properties
• 35b30
• 35b32
• 35j61