Solutions for Discrete Periodic Schrodinger Equations with Spectrum 0

被引：44

作者：

Yang, Minbo ^{[1
,2
]}

Chen, Wenxiong ^{[1
]}

Ding, Yanheng ^{[1
]}

机构：

[1] Chinese Acad Sci, AMSS, Inst Math, Beijing 100190, Peoples R China

[2] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Peoples R China

来源：

ACTA APPLICANDAE MATHEMATICAE | 2010年 / 110卷 / 03期

关键词：

Discrete Schrodinger equation; Standing waves; Nonlinear lattices; GAP SOLITONS; EXCITATION; SEQUENCES; EXISTENCE;

D O I：

10.1007/s10440-009-9521-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study the discrete nonlinear equation -Delta u(n) + epsilon(n)u(n) - omega u(n) = sigma chi(n)g(n)(u(n))u(n), where sigma = +/-1, Delta u(n) = u(n+1) + u(n-1) - 2u(n) is the discrete Laplacian in one spatial dimension. The sequences epsilon(n) and chi(n) are assumed to be N-periodic in n, i.e. epsilon(n+N) = epsilon(n) and chi(n+N) = chi(n). We prove the existence of solutions in l(2) for this equation with. a lower edge of a finite spectral gap and the nonlinearities satisfying very general superlinear assumptions.

引用

页码：1475 / 1488

页数：14

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