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.
Entire radial and nonradial solutions for systems with critical growth / Gladiali, Francesca; Grossi, Massimo; Troestler, Christophe. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - 57:2(2018), pp. -10.1007/s00526-018-1340-z. [10.1007/s00526-018-1340-z]
Entire radial and nonradial solutions for systems with critical growth
Grossi, MassimoMembro del Collaboration Group
;
2018
Abstract
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.| File | Dimensione | Formato | |
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