JournalsaihpcVol. 23, No. 6pp. 829–837

Ground states of nonlinear Schrödinger equations with potentials

  • Zhi-Qiang Wang

    School of Mathematics and Computer Sciences, Fujian Normal University, Fuzhou, 350007, PR China; Department of Mathematics and Statistics, Utah State University, Logan, UT 84322, USA

  • Jing Zeng

    School of Mathematics and Computer Sciences, Fujian Normal University, Fuzhou, 350007, PR China

  • Yongqing Li

    School of Mathematics and Computer Sciences, Fujian Normal University, Fuzhou, 350007, PR China
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Abstract

In this paper we study the nonlinear Schrödinger equation:

We give general conditions which assure the existence of ground state solutions. Under a Nehari type condition, we show that the standard Ambrosetti–Rabinowitz super-linear condition can be replaced by a more natural super-quadratic condition.

Résumé

Dans cet article nous étudions l'équation non-linéaire de Schrödinger :

Nous donnons les conditions générales qui garantissent l'existence de solutions d'énergie minimale. Sous une condition de type Nehari, nous démontrons que la condition super-linéaire d'Ambrosetti–Rabinowitz peut être remplacée par une condition super-quadratique plus naturelle.

Cite this article

Zhi-Qiang Wang, Jing Zeng, Yongqing Li, Ground states of nonlinear Schrödinger equations with potentials. Ann. Inst. H. Poincaré Anal. Non Linéaire 23 (2006), no. 6, pp. 829–837

DOI 10.1016/J.ANIHPC.2006.01.003