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Stability and bounded of solutions to non-autonomous delay differential equations of third order. (English) Zbl 1215.34079

Summary: 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

x (t)+a(t)φ(x ˙(t))x ¨(t)+b(t)ψ(x ˙(t))+c(t)h(x(t-r))=p(t,x(t),x(t-r),x ˙(t),x ˙(t-r),x ¨(t)),

when p(t,x(t),x(t-r),x ˙(t),x ˙(t-r),x ¨(t))=0 and p(t,x(t),x(t-r),x ˙(t),x ˙(t-r),x ¨(t))0, respectively. By using the Lyapunov functional approach, we prove two new results on the subject.

MSC:
34K12Growth, boundedness, comparison of solutions of functional-differential equations
34K20Stability theory of functional-differential equations
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