Results 91 to 100 of about 317,499 (205)

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  

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

On extreme values of Nehari manifold method via nonlinear Rayleigh's quotient [PDF]

arXiv, 2015
We study applicability conditions of the Nehari manifold method for the equation of the form $ D_u T(u)-\lambda D_u F(u)=0 $ in a Banach space $W$, where $\lambda$ is a real parameter. Our study is based on the development of the theory Rayleigh's quotient for nonlinear problems.
arxiv  

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
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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  

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  

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

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

The Nehari manifold method for Fractional Kirchhoff problem involving singular and exponential nonlinearity [PDF]

arXiv, 2020
In this paper we establish the existence of at least two weak solutions for the following fractional Kirchhoff problem involving singular and exponential nonlinearity \begin{equation*} \left\{\begin{split} M\left(\|u\|^{\frac{n}{s}}\right)(-\Delta)^s_{n/s}u & = \mu u^{-q}+ u^{r-1}\exp( u^{\beta})\;\text{in}\;\Om, u&>0,\;\text{in}\; \Om, u &= 0,\
arxiv  

Multiplicity of positive solutions for a Navier boundary-value problem involving the p-biharmonic with critical exponent

Electronic Journal of Differential Equations, 2011
By using the Nehari manifold and variational methods, we prove that a p-biharmonic system has at least two positive solutions when the pair the parameters satisfy certain inequality.
Ying Shen, Jihui Zhang
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