scholarly journals Convergence of ground state solutions for nonlinear Schrödinger equations on graphs

2018 ◽  
Vol 61 (8) ◽  
pp. 1481-1494 ◽  
Author(s):  
Ning Zhang ◽  
Liang Zhao
Keyword(s):  
Ground State ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Ground State Solutions ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger 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.

scholarly journals NONLINEAR SCHRÖDINGER EQUATIONS WITH UNBOUNDED AND DECAYING RADIAL POTENTIALS

2007 ◽  
Vol 09 (04) ◽  
pp. 571-583 ◽  
Author(s):  
JIABAO SU ◽  
ZHI-QIANG WANG ◽  
MICHEL WILLEM
Keyword(s):  
Sobolev Spaces ◽  
Ground State ◽  
Symmetric Functions ◽  
Weighted Sobolev Spaces ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Ground State Solutions ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations

We establish some embedding results of weighted Sobolev spaces of radially symmetric functions. The results are then used to obtain ground state solutions of nonlinear Schrödinger equations with unbounded and decaying radial potentials. Our work unifies and generalizes many existing partial results in the literature.

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