Ground State Solution for a Class of Choquard Equations Involving General Critical Growth Term

2021 ◽  
Author(s):  
He Zhang ◽  
Haibo Chen
Keyword(s):  
Ground State ◽  
Ground State Solution ◽  
Critical Growth ◽  
State Solution

scholarly journals Lions-type theorem of the p-Laplacian and applications

2021 ◽  
Vol 10 (1) ◽  
pp. 1178-1200
Author(s):  
Yu Su ◽  
Zhaosheng Feng
Keyword(s):  
Elliptic Equation ◽  
Ground State ◽  
Quasilinear Elliptic Equation ◽  
Type Theorem ◽  
Ground State Solution ◽  
Critical Growth ◽  
State Solution ◽  
Quasilinear Elliptic

Abstract In this article, our aim is to establish a generalized version of Lions-type theorem for the p-Laplacian. As an application of this theorem, we consider the existence of ground state solution for the quasilinear elliptic equation with the critical growth.

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} .

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