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arXiv · 0906.1440

Nonexistence of nonconstant global minimizers with limit at $\infty$ of semilinear elliptic equations in all of $R^N$

Salvador Villegas
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Abstract

We prove nonexistence of nonconstant global minimizers with limit at infinity of the semilinear elliptic equation $-Δu=f(u)$ in the whole $R^N$, where $f\in C^1(R)$ is a general nonlinearity and $N\geq 1$ is any dimension. As a corollary of this result, we establish nonexistence of nonconstant bounded radial global minimizers of the previous equation.

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Salvador Villegas. 2009-06-08. Nonexistence of nonconstant global minimizers with limit at $\infty$ of semilinear elliptic equations in all of $R^N$. https://arxiv.org/abs/0906.1440

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