On finding bifurcations for non-variational elliptic systems by the extended quotients method
| Autor: | Il'yasov, Yavdat |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 11 pages |
| Databáze: | arXiv |
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