[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.2013.50.3.839

POSITIVE RADIAL SOLUTIONS FOR A CLASS OF ELLIPTIC SYSTEMS CONCENTRATING ON SPHERES WITH POTENTIAL DECAY

Carriao, Paulo Cesar (Departamento de Matematica Universidade Federal de Minas Gerais)
Lisboa, Narciso Horta (Departamento de Ciencias Exatas Universidade Estadual de Montes Claros)
Miyagaki, Olimpio Hiroshi (Departamento de Matematica Universidade Federal de Juiz de Fora)

Publication Information

Bulletin of the Korean Mathematical Society / v.50, no.3, 2013 , pp. 839-865 More about this Journal

Abstract

We deal with the existence of positive radial solutions concentrating on spheres for the following class of elliptic system $$$\large(S) \hfill{400} \{\array{-{\varepsilon}^2{\Delta}u+V_1(x)u=K(x)Q_u(u,v)\;in\;\mathbb{R}^N,\\-{\varepsilon}^2{\Delta}v+V_2(x)v=K(x)Q_v(u,v)\;in\;\mathbb{R}^N,\\u,v{\in}W^{1,2}(\mathbb{R}^N),\;u,v$ $&$ $gt;0\;in\;\mathbb{R}^N,}$$$ where ${\varepsilon}$ is a small positive parameter; $V_1$ , $V_2{\in}C^0(\mathbb{R}^N,[0,{\infty}))$ and $K{\in}C^0(\mathbb{R}^N,[0,{\infty}))$ are radially symmetric potentials; Q is a $(p+1)$ -homogeneous function and p is subcritical, that is, 1 < $p$ < $2^*-1$ , where $2^*=2N/(N-2)$ is the critical Sobolev exponent for $N{\geq}3$ .

Keywords

Schr $\ddot{o}$ dinger operator; radial solution; variational method; singular perturbation;

Citations & Related Records

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