Standing wave solutions with a critical frequency for nonlinear Schrödinger equations

2003 ◽  
Author(s):  
Jaeyoung Byeon ◽  
Zhi-Qiang Wang
Keyword(s):  
Standing Wave ◽  
Critical Frequency ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Wave Solutions ◽  
Nonlinear Schrodinger Equations

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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