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Zbl 1212.34226
Tunç, Cemil
A new result on the stability of solutions of a nonlinear differential equation of third-order with finite lag. (English)
[J] Southeast Asian Bull. Math. 33, No. 5, 947-958 (2009). ISSN 0129-2021; ISSN 0219-175X/e

Summary: Criteria for uniform stability of the trivial solution of the nonlinear third order delay differential equation $$x'''(t)+a_1(t)x''(t)+a_2(t)\psi(x(t-r(t)),x'(t-r(t)))+a_3x(t)=0$$ are obtained by Lyapunov's second method. By constructing a Lyapunov functional, sufficient conditions are established which guarantee the trivial solution of this equation is uniformly stable.

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

Keywords: stability; Lyapunov functional; nonlinear differential equations

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