scholarly journals On Standing Wave Solutions for Discrete Nonlinear Schrödinger Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Guowei Sun
Keyword(s):  
Standing Waves ◽  
Nehari Manifold ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Wave Solutions ◽  
Nonlinear Schrodinger Equations ◽  
Discrete Nonlinear Schrödinger Equations ◽  
The Nehari Manifold

The purpose of this paper is to study a class of discrete nonlinear Schrödinger equations. Under a weak superlinearity condition at infinity instead of the classical Ambrosetti-Rabinowitz condition, the existence of standing waves of the equations is obtained by using the Nehari manifold approach.

scholarly journals On a class of nonlocal nonlinear Schrödinger equations with potential well

2019 ◽  
Vol 9 (1) ◽  
pp. 665-689 ◽  
Author(s):  
Tsung-fang Wu
Keyword(s):  
Eigenvalue Problems ◽  
Nehari Manifold ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Asymptotic Results ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
The Nehari Manifold ◽  
Nonlocal Nonlinear

Abstract In this paper we investigate the existence, multiplicity and asymptotic behavior of positive solution for the nonlocal nonlinear Schrödinger equations. We exploiting the relationship between the Nehari manifold and eigenvalue problems to discuss how the Nehari manifold changes as parameters μ, λ changes and show how existence, multiplicity and asymptotic results for positive solutions of the equation are linked to properties of the manifold.

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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