scholarly journals Ground state solution of a noncooperative elliptic system

2013 ◽  
pp. 237-247
Author(s):  
Cyril Joel Batkam
Keyword(s):  
Elliptic System ◽  
Ground State ◽  
Ground State Solution ◽  
State Solution ◽  
Noncooperative Elliptic System

scholarly journals On the Ground State to Hamiltonian Elliptic System with Choquard’s Nonlinear Term

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Wenbo Wang ◽  
Jianwen Zhou ◽  
Yongkun Li
Keyword(s):  
Elliptic System ◽  
Bounded Domain ◽  
Ground State ◽  
Nonlinear Term ◽  
Smooth Boundary ◽  
Ground State Solution ◽  
State Solution ◽  
Hamiltonian Elliptic System

In the present paper, we consider the following Hamiltonian elliptic system with Choquard’s nonlinear term −Δu+Vxu=∫ΩGvy/x−yβdygv in Ω,−Δv+Vxv=∫ΩFuy/x−yαdyfu in Ω,u=0,v=0 on ∂Ω,where Ω⊂ℝN is a bounded domain with a smooth boundary, 0<α<N, 0<β<N, and F is the primitive of f, similarly for G. By establishing a strongly indefinite variational setting, we prove that the above problem has a ground state solution.

Ground State for a Coupled Elliptic System with Critical Growth

2018 ◽  
Vol 18 (1) ◽  
pp. 1-15
Author(s):  
Huiling Wu ◽  
Yongqing Li
Keyword(s):  
Elliptic System ◽  
Ground State ◽  
Ground State Solution ◽  
Critical Growth ◽  
State Solution ◽  
Content Type ◽  
Critical Nonlinearities ◽  
Differentiable Functions ◽  
Graphic Content

Abstract We study the following coupled elliptic system with critical nonlinearities: \left\{\begin{aligned} &\displaystyle-\triangle{u}+u=f(u)+\beta h(u)K(v),&&% \displaystyle x\in{\mathbb{R}}^{N},\\ &\displaystyle-\triangle{v}+v=g(v)+\beta H(u)k(v),&&\displaystyle x\in{\mathbb% {R}}^{N},\\ &\displaystyle u,v\in H^{1}({\mathbb{R}}^{N}),\end{aligned}\right. where {\beta>0} ; f, g are differentiable functions with critical growth; and {H,K} are primitive functions of h and k, respectively. Under some assumptions on f, g, h and k, we obtain the existence of a positive ground state solution of this system for {N\geq 2} .

Exact Ground State Solution for Anyons with spin-$\frac {1}{2}$

1992 ◽  
Vol 17 (1) ◽  
pp. 107-110
Author(s):  
Shun-Qing Shen ◽  
J. Cai ◽  
Rui-Bao Tao
Keyword(s):  
Ground State ◽  
Ground State Solution ◽  
State Solution ◽  
Exact Ground State

Existence of a Ground State Solution for a Quasilinear Schrödinger Equation

2014 ◽  
Vol 14 (4) ◽  
Author(s):  
Xiang-dong Fang ◽  
Zhi-qing Han
Keyword(s):  
Schrödinger Equation ◽  
Ground State ◽  
Schrodinger Equation ◽  
Ground State Solution ◽  
State Solution ◽  
Quasilinear Schrödinger Equation

AbstractIn this paper we are concerned with the quasilinear Schrödinger equation−Δu + V(x)u − Δ(uwhere N ≥ 3, 4 < p < 4N/(N − 2), and V(x) and q(x) go to some positive limits V

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