Solutions of a Nonlinear Schrödinger Equation

D. G. de Figueiredo () and Y. H. Ding ()
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D. G. de Figueiredo: IMECC-UNICAMP, Dipartmento de Matematica
Y. H. Ding: Chinese Academy of Sciences, Institute of Mathematics, AMSS

A chapter in Djairo G. de Figueiredo - Selected Papers, 2002, pp 517-538 from Springer

Abstract: Abstract This paper deals with existence and multiplicity of solutions to the nonlinear Schrödinger equation of the type $$ - \Updelta u + (\lambda a(x) + a_{0} (x))u = f(x,\,u),\quad u\; \in \;H^{1} ({\mathbb{R}}^{N} ). $$ 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: Schrödinger equation; Multiple solutions; Variational method; Primary 35Q55; Secondary 58E05 (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-02856-9_34

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DOI: 10.1007/978-3-319-02856-9_34

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