Lα2-solutions for nonlinear Schrödinger equations associated with the Weinstein operator.

In this article, we study the Schrödinger equation associated with the Weinstein operator (SW). We prove that the problem (SW) is locally well-posed in L α 2 R + d + 1 of the subcritical case p ∈ 0 , 4 d + 2 α + 2 and we show that the equation (SW) is globally well-posed in the critical case p = 4 d + 2 α + 2 . [ABSTRACT FROM AUTHOR]