On Dancer's conjecture for stable solutions with sign-changing nonlinearity

2023/12/02 by Liu, Yong, Wang, Kelei, Wei, Juncheng +1
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2312.00998

Abstract

We establish a Liouville type result for stable solutions for a wide class of second order semilinear elliptic equations in ℝⁿ with sign-changing nonlinearity f. Under the hypothesis that the equation does not have any nonconstant one dimensional stable solution, and a further nondegeneracy condition of f at its zero points, we show that in any dimension, stable solutions of the equation must be constant. This partially answers a question raised by Dancer.

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