A remark on least energy solutions in 𝐑^{𝐍}

Jeanjean, Louis; Tanaka, Kazunaga

doi:10.1090/S0002-9939-02-06821-1

A remark on least energy solutions in $\mathbf {R}^N$
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Proc. Amer. Math. Soc. 131 (2003), 2399-2408 Request permission

Abstract:

We study a mountain pass characterization of least energy solutions of the following nonlinear scalar field equation in $\mathbf {R}^N$: \begin{equation*} -\Delta u = g(u), u \in H^1(\mathbf {R}^N), \end{equation*} where $N\geq 2$. Without the assumption of the monotonicity of $t\mapsto \frac {g(t)}{t}$, we show that the mountain pass value gives the least energy level.

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