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BIBTEX RIS

On a class of quasilinear Schrödinger equations with superlinear or asymptotically linear terms

2017; Elsevier BV; Volume: 263; Issue: 6 Linguagem: Inglês

10.1016/j.jde.2017.04.040

ISSN

1090-2732

Autores

Uberlândio B. Severo, Elisandra Gloss, Edcarlos D. da Silva,

Tópico(s)

Nonlinear Differential Equations Analysis

Resumo

We study the existence and nonexistence of nonzero solutions for the following class of quasilinear Schrödinger equations:−Δu+V(x)u+κ2[Δ(u2)]u=h(u),x∈RN, where κ>0 is a parameter, V(x) is a continuous potential which is large at infinity and the nonlinearity h can be asymptotically linear or superlinear at infinity. In order to prove our existence result we have applied minimax techniques together with careful L∞-estimates. Moreover, we prove a Pohozaev identity which justifies that 2⁎=2N/(N−2) is the critical exponent for this class of problems and it is also used to show nonexistence results.

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