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

Antonio Azzollini; Alessio Pomponio

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

Analysis of PDEs 2008-02-14 v1

Authors: Antonio Azzollini , Alessio Pomponio

Abstract

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.

Keywords

schrodinger equation nonlinear term positive solution ground state minimizing problem berestycki-lions hypotheses

Cite

@article{arxiv.0802.1844,
  title  = {On the Schrodinger equation in $R^N$ under the effect of a general nonlinear term},
  author = {Antonio Azzollini and Alessio Pomponio},
  journal= {arXiv preprint arXiv:0802.1844},
  year   = {2008}
}

Comments

18 pages

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