Bounded and $L^p$-Solutions to a Generalized Lienard Equation with Integrable Forcing Term

Abstract

This paper presents two theorems concerning the inhomogeneous differential equation $x'' + c(t) f(x) x' + a(t,x) = e(t)$, where $e(t)$ is a continuous absolutely integrable function. The first theorem gives sufficient conditions when all solutions to this equation are bounded while the second discusses when all solutions are in $L^p [0, \infty )$.