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.
Bartolucci, D., Yeyao, H., Jevnikar, A., Wen, Y. (2023). Generic properties of the Rabinowitz unbounded continuum. ADVANCED NONLINEAR STUDIES, 23(1) [10.1515/ans-2022-0062].
Generic properties of the Rabinowitz unbounded continuum
Bartolucci, Daniele;Jevnikar, Aleks;
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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