Boundedness of solutions to fourth-order differential equation with oscillatory restoring and forcing terms

Abstract

This paper concerns the fourth order differential equation x″″ + αx‴ + ƒ(x″) + g(x′) + h(x) = p(t) Using the Cauchy formula for the particular solution of non-homogeneous linear differential equations with constant coefficients, we prove that the solution and its derivatives up to order three are bounded.