scholarly journals GROUND STATE SOLUTIONS OF NONLINEAR SCHRÖDINGER EQUATIONS WITH ASYMPTOTICALLY PERIODIC POTENTIALS

2021 ◽  
Vol 11 (4) ◽  
pp. 1663-1677
Author(s):  
Jianmin Guo ◽  
◽  
Shugui Kang ◽  
Shiwang Ma ◽  
Guang Zhang ◽  
...  
Keyword(s):  
Ground State ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Ground State Solutions ◽  
Nonlinear Schrödinger ◽  
Periodic Potentials ◽  
Nonlinear Schrodinger Equations ◽  
Asymptotically Periodic

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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