Bounded and L2-solutions to a second order nonlinear differential equation with a square integrable forcing term

Abstract

This paper presents two theorems concerning the nonlinear differential equation x″+c(t)f(x)x′+a(t,x)=e(t), where e(t) is a continuous square-integrable function. The first theorem gives sufficient conditions when all the solutions of this equation are bounded while the second theorem discusses when all the solutions are in L2[0,∞).