Therefore, one can conclude that. That is,. This fact shows that all solutions of the equation considered are bounded.
We establish the following result. Then, there exists a finite positive constant K such that the solution x t of equation 1 defined by the initial functions. Now, in view of 4 , it follows that. Now, the estimates related to V 1 and V 2 yield. Now, let. Then, a direct computation along this solution shows that. In view of the assumptions of theorem and expression 5 , we have that.
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Making use of these inequalities, we get. Now, subject to the assumptions ii and iii of theorem, one easily finds that. Gathering the above discussion into 8 and making use of the assumption ii , it follows that.
In view of 7 , it follows that. Now, the inequality 7 and the last inequality together give that. This fact completes the proof of theorem.
Abou-El-Ela and A. Sadek, On the boundedness and periodicity of a certain differential equation of fifth order. Anwendungen, 11 2 , Academic Press, Orlando Chukwu, On the boundedness and stability of solutions of some differential equations of the fifth order. SIAM J. Translated from the Russian by Robert J. McLaughlin Holden-Day, Inc. Norkin, Introduction to the theory and application of differential equations with deviating arguments. Translated from the Russian by John L.
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Mathematics and its Applications, Kluwer Academic Publishers Group, Dordrecht Hale, Theory of Functional Differential Equations. Springer-Verlag, New York-Heidelberg Hale and S. Verduyn Lunel, Introduction to functional-differential equations. Applied Mathematical Sciences, Springer-Verlag, New York Kolmanovskii and A.http://d2.june.dns05.com/el-corazn-de-un-hombre-aspirantes-al.php
On the Stability of Solutions of Nonlinear Functional Differential Equation of the Fifth-Order
Kluwer Academic Publishers, Dordrecht Kolmanovskii and V. Nosov, Stability of functional-differential equations. Mathematics in Science and Engineering, Academic Press, Inc. Krasovskii, Stability of motion. Applications of Lyapunov's second method to differential systems and equations with delay.
Interval-valued functional differential equations under dissipative conditions
Translated by J. Liapunov, Stability of Motion. Academic Press, London Makay, On the asymptotic stability of the solutions of functional-differential equations with infinite delay. Differential Equations, 1 , Buy eBook. Buy Softcover. FAQ Policy. About this book Since the publication of my lecture notes, Functional Differential Equations in the Applied Mathematical Sciences series, many new developments have occurred.
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