On finding bifurcations for non-variational elliptic systems by the extended quotients method
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913341465690112 |
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| author | Il'yasov, Yavdat |
| author_facet | Il'yasov, Yavdat |
| contents | We develop a novel method for finding bifurcations for nonlinear systems of equations based on directly finding bifurcations through saddle points of extended quotients. The method is applied to find the saddle-node bifurcation point for elliptic equations with the nonlinearity of the general convex-concave type. The main result justifies the variational formula for the detection of the maximum saddle-node type bifurcation point of stable positive solutions. As a consequence, a precise threshold value separating the interval of the existence of stable positive solutions is established. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_02684 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On finding bifurcations for non-variational elliptic systems by the extended quotients method Il'yasov, Yavdat Analysis of PDEs Mathematical Physics We develop a novel method for finding bifurcations for nonlinear systems of equations based on directly finding bifurcations through saddle points of extended quotients. The method is applied to find the saddle-node bifurcation point for elliptic equations with the nonlinearity of the general convex-concave type. The main result justifies the variational formula for the detection of the maximum saddle-node type bifurcation point of stable positive solutions. As a consequence, a precise threshold value separating the interval of the existence of stable positive solutions is established. |
| title | On finding bifurcations for non-variational elliptic systems by the extended quotients method |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2405.02684 |