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Carriao, Paulo Cesar,Lisboa, Narciso Horta,Miyagaki, Olimpio Hiroshi Korean Mathematical Society 2013 대한수학회보 Vol.50 No.3
We deal with the existence of positive radial solutions concentrating on spheres for the following class of elliptic system $$\large(S) \hfill{400} \{\array{-{\varepsilon}^2{\Delta}u+V_1(x)u=K(x)Q_u(u,v)\;in\;\mathbb{R}^N,\\-{\varepsilon}^2{\Delta}v+V_2(x)v=K(x)Q_v(u,v)\;in\;\mathbb{R}^N,\\u,v{\in}W^{1,2}(\mathbb{R}^N),\;u,v>0\;in\;\mathbb{R}^N,}$$ 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 $N{\geq}3$.
Paulo Cesar Carriao,Olimpio Hiroshi Miyagaki,Narciso Horta Lisboa 대한수학회 2013 대한수학회보 Vol.50 No.3
We deal with the existence of positive radial solutions concentrating on spheres for the following class of elliptic system (S) [수식], where ε is a small positive parameter; V1, V2 ∈ C0(RN, [0,1)) and K 2 C0(RN, (0,∞)) 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 ≥ 3.