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

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

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