GROUND STATE SOLUTION TO THE SCHRODINGER EQUATION WITH MIXED TYPE NONLINEARITY. SHARP CRITERION FOR BLOW-UP AND GLOBAL EXISTENCE

摘要

We study the Cauchy problem for the focusing Schrodinger equation with a mixed local-nonlocal nonlinear term. We give conditions for finite time blow-up and for global existence in dependence of the initial data. In particular, we present a relationship between the best constant for a Gagliardo-Nirenberg type interpolation inequality and a sharp criterion for the existence of global solutions.