Results 61 to 70 of about 521 (162)

On the Existence of Ground State Solutions of the Periodic Discrete Coupled Nonlinear Schrödinger Lattice

Journal of Applied Mathematics, 2013
We study the existence of ground state solutions of the periodic discrete coupled nonlinear Schrödinger lattice by using the Nehari manifold approach combined with periodic approximations. We show that both of the components of the ground state solutions
Meihua Huang, Zhan Zhou
doaj   +1 more source

Ground states for Schrodinger-Poisson systems with three growth terms

Electronic Journal of Differential Equations, 2014
In this article we study the existence and nonexistence of ground states of the Schrodinger-Poisson system $$\displaylines{ -\Delta u+V(x)u+K(x)\phi u=Q(x)u^3,\quad x\in \mathbb{R}^3,\cr -\Delta\phi=K(x)u^2, \quad x\in \mathbb{R}^3, }$$ where V ...
Hui Zhang, Fubao Zhang, Junxiang Xu
doaj  

Positive solutions for weighted singularp-Laplace equations via Nehari manifolds [PDF]

Applicable Analysis, 2019
In this paper we study weighted singular $p$-Laplace equations involving a bounded weight function which can be discontinuous. Due to its discontinuity classical regularity results cannot be applied. Based on Nehari manifolds we prove the existence of at least two positive bounded solutions of such problems.
Nikolaos S. Papageorgiou, Patrick Winkert   +1 more
openaire   +3 more sources

Ground state solution of a nonlocal boundary-value problem

Electronic Journal of Differential Equations, 2013
In this article, we apply the Nehari manifold method to study the Kirchhoff type equation $$ -\Big(a+b\int_\Omega|\nabla u|^2dx\Big)\Delta u=f(x,u) $$ subject to Dirichlet boundary conditions.
Cyril Joel Batkam
doaj  

Ground state solutions for asymptotically periodic Schrodinger equations with critical growth

Electronic Journal of Differential Equations, 2013
Using the Nehari manifold and the concentration compactness principle, we study the existence of ground state solutions for asymptotically periodic Schrodinger equations with critical growth.
Hui Zhang, Junxiang Xu, Fubao Zhang
doaj  

Fractional minimization problem on the Nehari manifold

Electronic Journal of Differential Equations, 2018
In the framework of fractional Sobolev space, using Nehari manifold and concentration compactness principle, we study a minimization problem in the whole space involving the fractional Laplacian.
Mei Yu, Meina Zhang, Xia Zhang
doaj  

Solitary Waves of the Schrödinger Lattice System with Nonlinear Hopping

Journal of Function Spaces, 2015
This paper is concerned with the nonlinear Schrödinger lattice with nonlinear hopping. Via variation approach and the Nehari manifold argument, we obtain two types of solution: periodic ground state and localized ground state.
Ming Cheng
doaj   +1 more source

Non-Nehari manifold method for a class of generalized quasilinear Schrödinger equations

Applied Mathematics Letters, 2017
Abstract In this paper, we study the following generalized quasilinear Schrodinger equation − d i v ( g 2 ( u ) ∇ u ) + g ( u ) g ′ ( u ) | ∇ u | 2 + V ( x ) u = f ( x , u ) , x ∈ R N , where N ≥ 3 , 2 ∗ = 2 N N − 2 , g ∈
Jianhua Chen, Xianhua Tang, Bitao Cheng
openaire   +2 more sources

Periodic solutions for second-order even and noneven Hamiltonian systems

Boundary Value Problems
In this paper, we consider the second-order Hamiltonian system x ¨ + V ′ ( x ) = 0 , x ∈ R N . $$ \ddot{x}+V^{\prime}(x)=0,\quad x\in \mathbb{R}^{N}. $$ We use the monotonicity assumption introduced by Bartsch and Mederski (Arch. Ration. Mech. Anal.
Juan Xiao, Xueting Chen
doaj   +1 more source

On Standing Wave Solutions for Discrete Nonlinear Schrödinger Equations

Abstract and Applied Analysis, 2013
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 ...
Guowei Sun
doaj   +1 more source