Multiplicity of standing wave solutions of nonlinear Schrödinger equations with electromagnetic fields

2007 ◽  
Vol 59 (5) ◽  
pp. 810-833 ◽  
Author(s):  
Zhongwei Tang
Keyword(s):  
Standing Wave ◽  
Electromagnetic Fields ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Wave Solutions ◽  
Nonlinear Schrodinger Equations

Solutions of perturbed Schrödinger equations with electromagnetic fields and critical nonlinearity

2010 ◽  
Vol 54 (1) ◽  
pp. 131-147 ◽  
Author(s):  
Sihua Liang ◽  
Jihui Zhang
Keyword(s):  
Standing Wave ◽  
Electromagnetic Fields ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Critical Nonlinearity ◽  
Existence And Multiplicity ◽  
Wave Solutions ◽  
Nonlinear Schrodinger Equations ◽  
Image Position

AbstractWe consider the existence and multiplicity of standing-wave solutionsof nonlinear Schrödinger equations with electromagnetic fields and critical nonlinearityUnder suitable assumptions, we prove that it has at least one solution and that, for any m ∈ ℕ, it has at least m pairs of solutions.

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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