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) + φ(ẍ) ẍ· + ƒ(x, ẋ)ẍ + g(ẋ) + h(x) = p(t, x, ẋ, ẍ, ẍ·), when p ≡ 0 and when p ≠ 0. Our results include and improve some well-known results in the literature.