Bounded solutions to nonlinear delay differential equations of third order

Abstract

This paper gives some sufficient conditions for every solution of delay differential equation \begin{align*} \overset{\ldots}{x}(t) +f(t,x(t),x(t-r),\dot{x}(t),\dot{x}(t-r),\ddot{x}(t),\ddot{x}(t-r)) &+b(t)g(x(t-r),\dot{x}(t-r)) +c(t)h(x(t)) \\& =p(t,x(t),x(t-r),\dot{x}(t),\dot{x}(t-r),\ddot{x}(t)) \end{align*} to be bounded.