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In this paper, we study the Schr\"odinger equation associated with theWeinstein operators and we prove the existence and uniqueness of globalsolutions to Schr\"odinger-Weinstein equations in\\ $C\left(\left(-T_{\min },T_{\max }\right) ; L_{\alpha}^{2}\left(\mathbb{R}^{d+1}_+\right)\right) \bigcapL_{l o c}^{q_{1}}\left(\left(-T_{\min }, T_{\max }\right) ;L_{\alpha}^{r_{1}}\left(\mathbb{R}^{d+1}_+\right)\right)$ \\ on initialcondition in $L_{\alpha}^{2}\left(\mathbb{R}^{d+1}_+\right)$

$\mathrm{L}^{2}_{\alpha} $-Solutions for Nonlinear Schr\"odinger Equations Associated With The Weinstein Operator