Ground state solution of p-Laplacian equation with finite many critical nonlinearities

2020 ◽  
Vol 66 (2) ◽  
pp. 283-311 ◽  
Author(s):  
Yu Su ◽  
Haibo Chen ◽  
Senli Liu ◽  
Guofeng Che
2018 ◽  
Vol 18 (1) ◽  
pp. 1-15
Author(s):  
Huiling Wu ◽  
Yongqing Li

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} .


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

Sign in / Sign up

Export Citation Format

Share Document