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 $$ x^{(4)}+varphi (ddot{x})dddot{x}+f(x,dot{x}) ddot{x}+g(dot{x})+h(x)=p(t,x,dot{x},ddot{x},dddot{x}),, $$ when $pequiv 0$ and when $p eq 0$. Our results include and improve some well-known results in the literature.

Keywords

• Fourth order differential equations
• stability
• boundedness.