On the Schrodinger equation in $R^N$ under the effect of a general nonlinear term

Details On the Schrodinger equation in $R^N$ under the effect of a general nonlinear term On the Schrodinger equation in $R^N$ under the effect of a general nonlinear term

2008-02-13

arxiv.org/abs/0802.1844v1

Mathematics

Analysis of PDEs

18 pages

Scientific paper

In this paper we prove the existence of a positive solution to the equation
$-\Delta u + V(x)u=g(u)$ in $R^N,$ assuming the general hypotheses on the
nonlinearity introduced by Berestycki & Lions. Moreover we show that a
minimizing problem, related to the existence of a ground state, has no
solution.

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