PDF Introduction to the theory of functional differential equations

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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.

1 Introduction

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.

Mathematics in Science and Engineering, Vol. Gopalsamy, Stability and oscillations in delay differential equations of population dynamics.

Special Functions And Diff. Equation Course Evaluation

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.

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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.

Show all. Linear differential difference equations Pages Hale, Jack K. Retarded functional differential equations: basic theory Pages Hale, Jack K.

Functional Differential Equations: Advances and Applications

Properties of the solution map Pages Hale, Jack K. Autonomous and periodic processes Pages Hale, Jack K. Stability theory Pages Hale, Jack K. General linear systems Pages Hale, Jack K. Linear autonomous equations Pages Hale, Jack K. Linear periodic systems Pages Hale, Jack K. Perturbed linear systems Pages Hale, Jack K. Behavior near equilibrium and periodic orbits for autonomous equations Pages Hale, Jack K.

Periodic solutions of autonomous equations Pages Hale, Jack K. Equations of neutral type Pages Hale, Jack K. Global theory Pages Hale, Jack K. Show next xx.