In this paper we show the uniqueness of the critical point for semi-stable solutions of the problem{-Delta u = f(u) in Omegau > 0 in Omegau = 0 on partial derivative Omega,where Omega subset of R-2 is a smooth bounded domain whose boundary has nonnegative curvature and f(0) >= 0. It extends a result by Cabre-Chanillo to the case where the curvature of partial derivative Omega vanishes.
Uniqueness of the critical point for semi-stable solutions in R-2
De Regibus, F;
2021-01-01
Abstract
In this paper we show the uniqueness of the critical point for semi-stable solutions of the problem{-Delta u = f(u) in Omegau > 0 in Omegau = 0 on partial derivative Omega,where Omega subset of R-2 is a smooth bounded domain whose boundary has nonnegative curvature and f(0) >= 0. It extends a result by Cabre-Chanillo to the case where the curvature of partial derivative Omega vanishes.
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