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.
Generic properties of the Rabinowitz unbounded continuum
Jevnikar A.;
2023-01-01
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.File in questo prodotto:
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