Bull. Korean Math. Soc. 2013; 50(3): 839-865
Printed May 31, 2013
https://doi.org/10.4134/BKMS.2013.50.3.839
Copyright © The Korean Mathematical Society.
Paulo Cesar Carri\~{a}o, Narciso Horta Lisboa, and Olimpio Hiroshi Miyagaki
Universidade Federal de Minas Gerais, Universidade Estadual de Montes Claros, Universidade Federal de Juiz de Fora
We deal with the existence of positive radial solutions concentrating on spheres for the following class of elliptic system \begin{equation} \left\{ \begin{array}{c} -\varepsilon ^{2}\Delta u+V_{1}(x)u=K(x)Q_{u}(u,v)\text{ in } \mathbb{R} ^{N}\text{,} \\ -\varepsilon ^{2}\Delta v+V_{2}(x)v=K(x)Q_{v}(u,v)\text{ in } \mathbb{R} ^{N}\text{,} \\ u,v\in W^{1,2}( \mathbb{R} ^{N})\text{, }u,v>0\text{ in } \mathbb{R} ^{N}\text{,} \end{array} \right. \tag{$S$} \end{equation} where $\varepsilon $ is a small positive parameter; $V_{1}$, $V_{2}\in C^{0}( \mathbb{R} ^{N},\left[ 0,\infty \right) )$ and $K\in C^{0}( \mathbb{R} ^{N},\left( 0,\infty \right) )$ are radially symmetric potentials; $Q$ is a $ (p+1)$-homogeneous function and $p$ is subcritical, that is, $1
Keywords: Schr\"odinger operator, radial solution, variational method, singular perturbation
MSC numbers: 35J50, 35B06, 35A15, 35B25
2016; 53(3): 667-680
2015; 52(4): 1149-1167
2015; 52(2): 661-677
2014; 51(5): 1433-1451
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd