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

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

2009-06-08

arxiv.org/abs/0906.1440v1

Mathematics

Analysis of PDEs

6 pages

Scientific paper

We prove nonexistence of nonconstant global minimizers with limit at infinity
of the semilinear elliptic equation $-\Delta u=f(u)$ 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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