Stability and Boundedness of Solutions To Certain Fourth-Order Differential Equations

Abstract

We give criteria for the asymptotic stability and boundedness of solutions to the nonlinear fourth-order ordinary differential equation x((4)) + phi(x) x + f(x, x) x + g(x) + h(x) = p(t, x, x, x, x), when p equivalent to 0 and when p not equal 0. Our results include and improve some well-known results in the literature.