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Zbl 1178.34080
Tunç, Cemil
A new boundedness result to nonlinear differential equations of third order with finite lag. (English)
[J] Commun. Appl. Anal. 13, No. 1, 1-10 (2009). ISSN 1083-2564

Summary: Criteria for boundedness of solutions to the nonlinear third order delay differential equation $$\multline x'''(t) + y(x(t),x''(t), x''(t))x''(t) +\psi(x(t - r(t)),\ x'(t - r(t))) + h(x(t - r(t))) =\\ = p(t, x(t),x(t- r(t)),x'(t),x'(t - r(t)), x''(t))\endmultline$$ are obtained by Lyapunov's second method. By introducing a Lyapunov functional, sufficient conditions are established that guarantee that all solutions of this equation are bounded. An example is also given to illustrate the importance of result obtained.

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

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