6.—Oscillation Theory for Semilinear Schrödinger Equations and Inequalities

Synopsis Sufficient conditions are derived for every solution of a nonlinear Schrödinger equation (or inequality) to be oscillatory in an exterior domain of E n . Such results apply in particular to the n -dimensional Emden-Fowler equation. The method involves oscillatory behaviour of solutions of a nonlinear ordinary differential inequality satisfied by the spherical mean of a positive solution of the Schrödinger equation.