The Cauchy problem for a semilinear ordinary differential equation in the homogeneous and isotropic spacetime

Abstract

A semilinear ordinary differential equation is derived from a semilinear Schrödinger equation in the homogeneous and isotropic spacetime by the Ehrenfest theorem. The Cauchy problem for the equation is considered. Exact solutions and nonexistence of global weak solutions of the equation are also considered in the de Sitter spacetime. The effects of spatial expansion and contraction are studied.