ON THE BLOW-UP SOLUTIONS FOR THE NONLINEAR RADIAL SCHRÖDINGER EQUATIONS WITH SPATIAL VARIABLE COEFFICIENTS

Abstract

We study a generalized nonlinear Schrödinger equations with spatial variable coefficients, which models the remarkable inhomogeneous Schrö dinger maps (ISM). A new weighted Sobolev space W^(ℝ⁺) is introduced and the existence of blow-up solutions of this equations, including the integrable radial ISM, with the initial data in W^(ℝ⁺) is proved