Generic properties of the Rabinowitz continuum
Daniele Bartolucci, Yeyao Hu, Aleks Jevnikar, Wen Yang
TL;DR
This paper demonstrates that, under generic domain variations, the Rabinowitz continuum of solutions to a nonlinear eigenvalue problem forms a simple analytic curve, resembling the classic Gel'fand problem in two dimensions.
Contribution
It establishes that the Rabinowitz continuum is generically a simple analytic curve under domain variations, extending understanding of global bifurcation diagrams.
Findings
The Rabinowitz continuum is generically a simple analytic curve.
The bifurcation diagram resembles the Gel'fand problem in two dimensions.
The result applies to nonlinear eigenvalue problems under domain variations.
Abstract
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.
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Taxonomy
TopicsStability and Controllability of Differential Equations · Contact Mechanics and Variational Inequalities · Advanced Numerical Methods in Computational Mathematics