Abstract
In this paper, we obtain some sufficient conditions to guarantee the uniform asymptotic stability of zero solution and bounded of all solutions to non-autonomous delay differential equation of third order $$\begin{array}{@{}ll}\vspace*{-1pt}&\dddot{x}(t)+a(t)\varphi\bigl(\dot{x}(t)\bigr)\ddot{x}(t)+b(t)\psi\bigl(\dot{x}(t)\bigr)\\[5pt]&\qquad{}+c(t)h\bigl(x(t-r)\bigr)\\[5pt]&\quad =p\bigl(t,x(t),x(t-r),\dot{x}(t),\dot{x}(t-r),\ddot{x}(t)\bigr),\vspace*{-1pt}\end{array}$$ when $p(t,x(t),x(t-r),\dot{x}(t),\dot{x}(t-r),\ddot{x}(t))=0$ and $p(t,x(t),x(t-r),\dot{x}(t),\dot{x}(t-r),\ddot{x}(t))\ne 0$ , respectively. By using the Liapunov functional approach, we prove two new results on the subject.
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