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arXiv · 1902.03484

Non-uniqueness of blowing-up solutions to the Gelfand problem

Luca Battaglia·Massimo Grossi·Angela Pistoia
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Abstract

We consider the Gelfand problem on a planar domain. Under some conditions on the potential, we provide the first examples of multiplicity for blowing-up solutions at a given point in the domain. The argument is based on a refined Lyapunov-Schmidt reduction and the computation of the degree of a finite-dimensional map.

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Luca Battaglia, Massimo Grossi, Angela Pistoia. 2019-02-09. Non-uniqueness of blowing-up solutions to the Gelfand problem. https://arxiv.org/abs/1902.03484

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