GLOBAL EXISTENCE AND BLOW-UP FOR THE FOCUSING INHOMOGENEOUS NONLINEAR SCHRODINGER EQUATION WITH INVERSE-SQUARE POTENTIAL

In this paper, we study the Cauchy problem for the focusing inhomogeneous nonlinear Schrodinger equation with inverse-square potential iu(t) + Delta u - c|x|(-2)u + |x|(-b)|u|(sigma) u = 0; u(0) = u(0) is an element of H-c(1), (t, x) is an element of R x R-d, where d >= 3, 0 < b < 2, 4-2b/d < sigma < 4-2b/d-2 and c > -c(d) := -(d-2/2)(2). We first establish the criteria for global existence and blow-up of general (not necessarily radial or finite variance) solutions to the equation. Using these criteria, we study the global existence and blow-up of solutions to the equation with general data lying below, at, and above the ground state threshold. Our results extend the global existence and blow-up results of Campos-Guzman (Z. Angew. Math. Phys., 2021) and Dinh-Keraani (SIAM J. Math. Anal., 2021).