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- W2337334998 abstract "In the present paper we consider the coupled system of nonlinear Schrodinger equations with the fractional Laplacian [ left{ begin{aligned} (-Delta)^alpha u_1 & = lambda_1u_1+f_1(u_1)+partial_1F(u_1,u_2) mathrm{in} mathbb{R}^N, (-Delta)^alpha u_2 & = lambda_2u_2+f_2(u_2)+partial_2F(u_1,u_2) mathrm{in} mathbb{R}^N, end{aligned} right. ] where $u_1, u_2:mathbb{R}^Nto mathbb{C}, Ngeq 2,$ and $0 0.$ The numbers $lambda_1$ and $lambda_2$ in the system appear as Lagrange multiplier. The method is based on the concentration compactness arguments, but introduces a new way to verify some of the properties of the variational problem that are required in order for the concentration compactness method to work. We consider the case when $f_j(s)=mu_j|s|^{p_j-2}s$ and $F(s,t)=beta |s|^{r_1}|t|^{r_2}$ with $mu_j>0, beta>0,$ and the values $r_i>1, 2<p_j, r_1+r_2<2+frac{4alpha}{N}.$ The method also enables us to prove the stability result of standing wave solutions associated with the set of global minimizers." @default.
- W2337334998 created "2016-06-24" @default.
- W2337334998 creator A5057620283 @default.
- W2337334998 date "2016-04-06" @default.
- W2337334998 modified "2023-09-27" @default.
- W2337334998 title "Existence and stability of standing waves for nonlinear Schrodinger systems involving the fractional Laplacian" @default.
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