scholarly journals On Standing Wave Solutions for Discrete Nonlinear Schrödinger Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Guowei Sun

The purpose of this paper is to study a class of discrete nonlinear Schrödinger equations. Under a weak superlinearity condition at infinity instead of the classical Ambrosetti-Rabinowitz condition, the existence of standing waves of the equations is obtained by using the Nehari manifold approach.

2019 ◽  
Vol 9 (1) ◽  
pp. 665-689 ◽  
Author(s):  
Tsung-fang Wu

Abstract In this paper we investigate the existence, multiplicity and asymptotic behavior of positive solution for the nonlocal nonlinear Schrödinger equations. We exploiting the relationship between the Nehari manifold and eigenvalue problems to discuss how the Nehari manifold changes as parameters μ, λ changes and show how existence, multiplicity and asymptotic results for positive solutions of the equation are linked to properties of the manifold.


2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Ali Mai ◽  
Zhan Zhou

We consider the periodic discrete nonlinear Schrödinger equations with the temporal frequency belonging to a spectral gap. By using the generalized Nehari manifold approach developed by Szulkin and Weth, we prove the existence of ground state solutions of the equations. We obtain infinitely many geometrically distinct solutions of the equations when specially the nonlinearity is odd. The classical Ambrosetti-Rabinowitz superlinear condition is improved.


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