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arXiv · 2405.02684

On finding bifurcations for non-variational elliptic systems by the extended quotients method

Yavdat Il'yasov
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Abstract

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.

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Yavdat Il'yasov. 2024-05-04. On finding bifurcations for non-variational elliptic systems by the extended quotients method. https://arxiv.org/abs/2405.02684

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