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

Abstract

This article concerns the fourth order differential equation x(iv) + ⍺x‴ + bx″ + 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 solutions and its derivatives up to order three are bounded.