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r_1|u_1|^{r_1-2}u_1|u_2|^{r_2}, \\\\ -\\Delta u_2 + (x_1^2+x_2^2)u_2&= \\lambda_2 u_2 + \\mu_2 |u_2|^{p_2 -2}u_2\n  +\\beta r_2 |u_1|^{r_1}|u_2|^{r_2 -2}u_2, \\end{aligned} \\right. \\end{equation*} under the constraint \\begin{align*} \\int_{\\mathbb{R}^3}|u_1|^2 \\, dx = a_1>0,\\quad \\int_{\\mathbb{R}^3}|u_2|^2 \\, dx = a_2>0, \\end{align*} where $\\mu_1, \\mu_2, \\beta >0, 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