MR2918146
Dragoş-Pătru COVEI
Dragoş-Pătru COVEI
Radial and Nonradial Solutions for a Semilinear Elliptic System of Schrödinger Type
Funkcialaj Ekvacioj. Serio Internacia
54
2011
439--449
http://fe.math.kobe-u.ac.jp/FE/FullPapers/54-3/54_439.pdf
http://www.ams.org/mathscinet-getitem?mr=MR2918146
In this article we consider the system of equations $\Delta u_i=p_i(x)f_i(u_1,\ldots,u_d)$ for $i=1,\ldots,d$ on $\mathbb{R}^N$, $N\geq 3$ and $d\in\{1,2,3,4,\ldots\}$. We prove that the considered system has a bounded positive entire solution under some conditions on $p_i$ and $f_i$. Also, we give a necessary condition as well as a sufficient condition for a positive radial solution to be large. The method of proving theorems is essentially based on a successive approximation. Furthermore, a non-radially symmetric solution is obtained by using a lower and upper solution method.
Entire solution, Large solution, Elliptic system.
35J61, 35J91.
54-439
2011
Radial and Nonradial Solutions for a Semilinear Elliptic System of Schrödinger Type
Dragoş-Pătru COVEI
Dragoş-Pătru COVEI
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