Existence and uniqueness of a saddle-node bifurcation point for nonlinear equations in general domains

Yavdat Il'yasov

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arXiv · 2404.05643

Existence and uniqueness of a saddle-node bifurcation point for nonlinear equations in general domains

Yavdat Il'yasov

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Abstract

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.

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Yavdat Il'yasov. 2024-04-08. Existence and uniqueness of a saddle-node bifurcation point for nonlinear equations in general domains. https://arxiv.org/abs/2404.05643

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