Ricerc@Sapienza

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