Ground State and Geometrically Distinct Solitons of Discrete Nonlinear Schrödinger Equations with Saturable Nonlinearities

2013 ◽  
Vol 131 (4) ◽  
pp. 389-413 ◽  
Author(s):  
Guanwei Chen ◽  
Shiwang Ma
Keyword(s):  
Ground State ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
Discrete Nonlinear Schrödinger Equations

scholarly journals Ground State Solutions for the Periodic Discrete Nonlinear Schrödinger Equations with Superlinear Nonlinearities

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Ali Mai ◽  
Zhan Zhou
Keyword(s):  
Ground State ◽  
Temporal Frequency ◽  
Nehari Manifold ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Ground State Solutions ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
Discrete Nonlinear Schrödinger Equations

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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