scholarly journals Standing wave solutions for the discrete nonlinear Schrödinger equations with indefinite sign subquadratic potentials

2016 ◽  
Vol 58 ◽  
pp. 95-102 ◽  
Author(s):  
Haiping Shi ◽  
Yuanbiao Zhang
Keyword(s):  
Standing Wave ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Wave Solutions ◽  
Nonlinear Schrodinger Equations ◽  
Discrete Nonlinear Schrödinger Equations

scholarly journals On Standing Wave Solutions for Discrete Nonlinear Schrödinger Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Guowei Sun
Keyword(s):  
Standing Waves ◽  
Nehari Manifold ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Wave Solutions ◽  
Nonlinear Schrodinger Equations ◽  
Discrete Nonlinear Schrödinger Equations ◽  
The Nehari Manifold

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.

scholarly journals Standing Wave Solutions for the Discrete Coupled Nonlinear Schrödinger Equations with Unbounded Potentials

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Meihua Huang ◽  
Zhan Zhou
Keyword(s):  
Standing Wave ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Compact Embedding ◽  
Schrödinger Equations ◽  
Coupled Nonlinear Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Wave Solutions ◽  
Nonlinear Schrodinger Equations ◽  
Coupled Nonlinear Schrodinger Equations

We demonstrate the existence of standing wave solutions of the discrete coupled nonlinear Schrödinger equations with unbounded potentials by using the Nehari manifold approach and the compact embedding theorem. Sufficient conditions are established to show that the standing wave solutions have both of the components not identically zero.

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