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arXiv · 1611.03584

Flat solutions of some non-Lipschitz autonomous semilinear equations may be stable for $N\geq 3$

Jesús Ildefonso Díaz·Jesús Hernández·Yavdat Il'yasov
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Abstract

We prove that flat ground state solutions ($i.e.$ minimizing the energy and with gradient vanishing on the boundary of the domain) of the Dirichlet problem associated to some semilinear autonomous elliptic equations with a strong absorption term given by a non-Lipschitz function are unstable for dimensions $N=1,2$ and they can be stable for $N\geq 3$ for suitable values of the involved exponents.

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Jesús Ildefonso Díaz, Jesús Hernández, Yavdat Il'yasov. 2016-11-11. Flat solutions of some non-Lipschitz autonomous semilinear equations may be stable for $N\geq 3$. https://arxiv.org/abs/1611.03584

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