Infinitely many segregated vector solutions of Schrodinger system

Abstract

We consider the following system of Schrödinger equations \begin{equation*}\left.\begin{cases} -ΔU + λU = α_0 U^3+ βUV^2 -ΔV + μ(y) V = α_1 V^3+βU^2V \end{cases}\right. \text{in} \quad \mathbb{R}^N, \ N=2, 3,\end{equation*} where $\lambda$, ${\alpha }_0$, ${\alpha }_1>0$ are positive constants, $\beta \in \mathbb{R}$ is the coupling constant, and $\mu :{\mathbb{R}}^N\to \mathbb{R}$ is a potential function. Continuing the work of Lin and Peng \cite{lin_peng_2014}, we present a solution of the type where one species has a peak at the origin and the other species has many peaks over a circle, but as seen in the above, coupling terms are nonlinear.