American Institute of Mathematical Sciences

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July  2002, 8(3): 563-584. doi: 10.3934/dcds.2002.8.563

Solutions of a nonlinear Schrödinger equation

D.G. deFigueiredo 1, and  Yanheng Ding 2,

1. 

Dipartmento de Matematica, IMECC-UNICAMP, 13081-970 Campinas S.P., Brazil
2. 

Institute of Mathematics, AMSS, Chinese Academy of Sciences, Beijing 100080, China

Received  February 2001 Revised  July 2001 Published  April 2002

This paper deals with existence and multiplicity of solutions to the nonlinear Schrödinger equation of the type

$-\Delta u + (\lambda a(x) + a_0(x))u = f(x, u), u\in H^1(\mathbb R^N).$

We improve some previous results in two respects: we do not require $a_0$ to be positive on one hand, and allow $f(x, u)$ to be critical nonlinear on the other hand.

Keywords: variational method., Schrödinger equation, multiple solutions.
Mathematics Subject Classification: Primary: 35Q55; Secondary: 58E0.
Citation: D.G. deFigueiredo, Yanheng Ding. Solutions of a nonlinear Schrödinger equation. Discrete & Continuous Dynamical Systems, 2002, 8 (3) : 563-584. doi: 10.3934/dcds.2002.8.563
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