Calculus of Variations and Geometric Measure Theory

D. Bartolucci - Y. Hu - A. Jevnikar - W. Yang

Generic properties of the Rabinowitz continuum

created by jevnikar on 16 Jul 2022
modified on 23 Mar 2023


Accepted Paper

Inserted: 16 jul 2022
Last Updated: 23 mar 2023

Journal: Adv. Nonlinear Stud.
Year: 2023


In this paper we prove that generically, in the sense of domain variations, the unbounded Rabinowitz continuum of solutions to a nonlinear eigenvalue problem is a simple analytic curve. The global bifurcation diagram resembles the classic model case of the Gel'fand problem in dimension two.

Keywords: bifurcation analysis, generic properties, Rabinowitz continuum