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

Salvador Villegas

doi:10.3934/cpaa.2011.10.1817

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2011, Volume 10, Issue 6: 1817-1821. Doi: 10.3934/cpaa.2011.10.1817

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

Salvador Villegas^1,

1.
Departamento de Análisis Matemático, Universidad de Granada, 18071, Granada

Received: March 31, 2010

Revised: February 28, 2011

Published: October 2011

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Abstract

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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Mathematics Subject Classification: Primary: 35J60, 26D10; Secondary: 35B35, 35J20.

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References

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