Solutions of a nonlinear Schrödinger equation

D.G. deFigueiredo; Yanheng Ding

doi:10.3934/dcds.2002.8.563

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2002, Volume 8, Issue 3: 563-584. Doi: 10.3934/dcds.2002.8.563

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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.
2.
Institute of Mathematics, AMSS, Chinese Academy of Sciences, Beijing 100080

Received: January 31, 2001

Revised: June 30, 2001

Published: June 2002

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Abstract

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.

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Mathematics Subject Classification: Primary: 35Q55; Secondary: 58E05.

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