Scattering results for the inhomogeneous nonlinear Schrodinger equation

In this paper, we establish new results on the global existence and scattering or non-scattering for the inhomogeneous nonlinear Schrodinger equation i partial derivative(t)u+Delta u = mu|x|(-b)|u|(alpha)u, in R-N, where N >= 3,mu is an element of C,0 < b < min(2,N-2) and 0 < alpha < (4-2b)/(N-2). In particular, we solve a problem left open in a previous study. More precisely, for the defocusing case, using the pseudo-conformal transformation, we prove the scattering for the Strauss exponent. Furthermore, for a class of initial data in H-s(R-N) and mu is an element of C, we establish that if 4-2b/N+2+2s < alpha < 4-2b/N, where s is an element of [0,s(0)] and s(0)>0 is a critical value, global existence and scattering occur for small initial data. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.