Standing waves for discrete Schrödinger equations in infinite lattices with saturable nonlinearities

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• 作者：Guanwei Chen^a ; ^{guanweic@163.com" class="auth_mail" title="E-mail the corresponding author} ; Shiwang Ma^b ; ^{shiwangm@163.net" class="auth_mail" title="E-mail the corresponding author} ; Zhi-Qiang Wang^c ; ^{zhi-qiang.wang@usu.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：35Q51 ; 35Q55 ; 39A12 ; 39A70
• 刊名：Journal of Differential Equations
• 出版年：2016
• 出版时间：15 September 2016
• 年：2016
• 卷：261
• 期：6
• 页码：3493-3518
• 全文大小：391 K

文摘

In this paper, we consider the periodic discrete nonlinear equation where L   is a Jacobi operator, and the nonlinearities g_n(s)$g_n(s)$ are asymptotically linear as |s|→∞$|s|\to \infty$. In the two different cases (ω is a spectral endpoint of L, or it belongs to a finite spectral gap of L), we obtain the existence of nontrivial solitons of this equation by using variational methods. In particular, a necessary and sufficient condition is obtained for the existence of gap solitons of the nonlinear equation. Here, solitons appear when we look for standing waves of some discrete nonlinear Schrödinger equations.