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Bounded solutions to nonlinear delay differential equations of third order. (English) Zbl 1187.34088

This paper gives sufficient conditions for every solution of the delay differential equation
\[ \begin{split} \ddot(t)+f(t, x(t), x(t - r),\dot x(t),\dot x(t - r),\ddot x(t),\ddot x(t - r))+b(t)g(x(t - r),x(t - r)) + c(t)h(x(t))=\\ p(t,x(t), x(t -r),\dot x(t),\dot x(t -r), \ddot x(t))\end{split} \]
to be bounded.

MSC:

34K12 Growth, boundedness, comparison of solutions to functional-differential equations
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