Generic properties of the Rabinowitz unbounded continuum
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 solutio...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2023-04-01
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| Series: | Advanced Nonlinear Studies |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/ans-2022-0062 |
| Summary: | 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. |
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| ISSN: | 2169-0375 |