Entire radial and nonradial solutions for systems with critical growth

Abstract

In this paper we establish existence of radial and nonradial solutions to the system $$ \begin{array}{ll} -\Delta u_1 = F_1(u_1,u_2) &\text{in }\mathbb{R}^N,\newline -\Delta u_2 = F_2(u_1,u_2) &\text{in }\mathbb{R}^N,\newline u_1\geq 0,\ u_2\geq 0 &\text{in }\mathbb{R}^N,\newline u_1,u_2\in D^{1,2}(\mathbb{R}^N), \end{array} $$ where $F_1,F_2$ are nonlinearities with critical behavior.