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Zbl 1202.34130
Tunç, Cemil
On some qualitative behaviors of solutions to a kind of third order nonlinear delay differential equations. (English)
[J] Electron. J. Qual. Theory Differ. Equ. 2010, Paper No. 12, 19 p., electronic only (2010). ISSN 1417-3875/e

Summary: Sufficient criteria are established to ensure the asymptotic stability and boundedness of solutions to third-order nonlinear delay differential equations of the form $$\multline \dddot{x}(t)+e(x(t), \dot{x}(t),\ddot{x}(t))\ddot{x}(t)+g(x(t-r),\dot{x} (t-r))+\psi (x(t-r))=\\ =p(t,x(t),x(t-r),x'(t),x'(t-r),x''(t)).\endmultline$$ By using Lyapunov's functional approach, we obtain two new results on the subject, which include and improve some related results in the relevant literature. Two examples are also given to illustrate the importance of results obtained.

MSC 2000:: *34K20 Stability theory of functional-differential equations
34K12 Properties of solutions of functional-differential equations

Keywords: delay differential equation of third order; Lyapunov functional; stability; boundedness

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