Existence and uniqueness of a saddle-node bifurcation point for nonlinear equations in general domains
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909163391549440 |
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| author | Il'yasov, Yavdat |
| author_facet | Il'yasov, Yavdat |
| contents | This paper provides a direct method of establishing the existence and uniqueness of saddle-node bifurcations for nonlinear equations in general domains. The method employs the scaled extended quotient whose saddle points correspond to the saddle-node bifurcations. The uniqueness of the saddle-node bifurcation point directly stems from the uniqueness of the saddle point. The method is applied to solving open problems involving the existence and uniqueness of the maximum saddle-node bifurcation for the positive solutions curve to an elliptic boundary value problem with a convex-concave nonlinearity in general domains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_05643 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence and uniqueness of a saddle-node bifurcation point for nonlinear equations in general domains Il'yasov, Yavdat Analysis of PDEs Mathematical Physics Chaotic Dynamics 35J60, 35J25, 35J61, 35B32 This paper provides a direct method of establishing the existence and uniqueness of saddle-node bifurcations for nonlinear equations in general domains. The method employs the scaled extended quotient whose saddle points correspond to the saddle-node bifurcations. The uniqueness of the saddle-node bifurcation point directly stems from the uniqueness of the saddle point. The method is applied to solving open problems involving the existence and uniqueness of the maximum saddle-node bifurcation for the positive solutions curve to an elliptic boundary value problem with a convex-concave nonlinearity in general domains. |
| title | Existence and uniqueness of a saddle-node bifurcation point for nonlinear equations in general domains |
| topic | Analysis of PDEs Mathematical Physics Chaotic Dynamics 35J60, 35J25, 35J61, 35B32 |
| url | https://arxiv.org/abs/2404.05643 |