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u_1^2u_2+\\kappa u_1~\\hbox{in}~ \\mathbb{R}^3,\n  u_1\\in H^1(\\mathbb{R}^3), u_2\\in H^1(\\mathbb{R}^3),\\nonumber \\end{cases} \\end{equation} under the constraint \\begin{equation} \\int_{\\mathbb{R}^3} u_1^2=a_1^2,~\\int_{\\mathbb{R}^3} u_2^2=a_2^2\\nonumber, \\end{equation} where 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solutions to Schr\\\"{o}dinger systems with potentials","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Zhaoyang Yun","submitted_at":"2024-06-19T04:23:28Z","abstract_excerpt":"In this paper, we study the normalized solutions of the Schr\\\"{o}dinger system with trapping potentials \\begin{equation}\\label{eq:diricichlet} \\begin{cases} -\\Delta u_1+V_1(x)u_1-\\lambda_1 u_1=\\mu_1 u_1^3+\\beta u_1u_2^{2}+\\kappa u_2~\\hbox{in}~ \\mathbb{R}^3,\\\\ -\\Delta u_2+V_2(x)u_2-\\lambda_2 u_2=\\mu_2 u_2^3+\\beta u_1^2u_2+\\kappa u_1~\\hbox{in}~ \\mathbb{R}^3,\n  u_1\\in H^1(\\mathbb{R}^3), u_2\\in H^1(\\mathbb{R}^3),\\nonumber \\end{cases} \\end{equation} under the constraint \\begin{equation} \\int_{\\mathbb{R}^3} u_1^2=a_1^2,~\\int_{\\mathbb{R}^3} u_2^2=a_2^2\\nonumber, \\end{equation} where 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