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Field name	Details
Dewey Class	515
Title	Functional Differential Equations ([EBook] /) / by Jack K. Hale.
Author	Hale, Jack K.
Other name(s)	SpringerLink (Online service)
Publication	New York, NY : : Springer US, , 1971.
Physical Details	238 p. : online resource.
Series	Applied mathematical sciences 0066-5452 ; ; 3
ISBN	9781461599685
Summary Note	It is hoped that these notes will serve as an introduction to the subject of functional differential equations. The topics are very selective and represent only one particular viewpoint. Complementary material dealing with extensions of closely related topics are given in the notes at the end. A short bibliography is appended as source material for further study. The author is very grateful to the Mathematics Department at UCLA for having extended the invitation to give a series of lectures on functional differ ential equations during the Applied Mathematics Year, 1968-1969. The extreme interest and sincere criticism of the members of the audience were a constant source of inspiration in the preparation of the lectures as well as the notes. Except for Sections 6, 32, 33, 34 and some other minor modifications, the notes represent the material covered in two quarters at UCLA. The author wishes to thank Katherine McDougall and Sandra Spinacci for their excellent preparation of the text. The author is also indebted to Eleanor Addison for her work on the drawings and to Dr. H. T. Banks for his careful proofreading of this material. Jack K. Hale Providence March 4, 1971 v TABLE OF CONTENTS 1. INTRODUCTION •••••.•..••.•••••••••.•••..•.••••••.••••••.••.••.•••.••• 1 2 • A GENERAL INITIAL VALUE PROBLEM 11 3 • EXISTENCE 13 4. CONTINUATION OF SOLUTIONS 16 CONTINUOUS DEPENDENCE AND UNIQUENESS 21 5.:
Contents note	1. Introduction -- 2. A General Initial Value Problem -- 3. Existence -- 4. Continuation of Solutions -- 5. Continuous Dependence and Uniqueness -- 6. Backward Continuation -- 7. Caratheodory Conditions -- 8. Remarks on the Map Defined by Solutions -- 9. Autonomous Systems -- 10. Definitions of Stability -- 11. Sufficient Conditions for Stability of General Systems -- 12. Sufficient Conditions for Instability -- 13. Stability in Autonomous Systems -- 14. An Example of Levin and Nohel -- 15. An Equation of Volterra -- 16. Nonhomogeneous Linear Systems -- 17. The “Adjoint” Equation and Representation of Solutions -- 18. Stability of Perturbed Systems -- 19. Linear Autonomous Equations. The Semigroup and Infinitesimal Generator -- 20. The Eigenvalues of a Linear Autonomous Equation. Decomposition of C -- 21. Decomposing C with the Adjoint Equation -- 22. Estimates on the Complementary Subspace -- 23. An Example -- 24. The Decomposition in the Variation of Constants Formula -- 25. Forced Linear Systems -- 26. The Saddle Point Property -- 27. A Fixed Point Theorem for Cones -- 28. A Periodicity Theorem for Functional Equations -- 29. The Equation $${\rm{\dot x}}\left( {\rm{t}} \right) = - \alpha {\rm{x}}\left( {{\rm{t}} - 1} \right)\left[ {{\rm{l}} + {\rm{x}}\left( {\rm{t}} \right)} \right]$$ -- 30. The Equation $${\rm{\dot x}}\left( {\rm{t}} \right) = - \alpha {\rm{x}}\left( {{\rm{t}} - 1} \right)\left[ {{\rm{l}} + {\rm{x}} 2 \left( {\rm{t}} \right)} \right]$$ -- 31. The Equation $${\rm{\ddot x}}\left( {\rm{t}} \right) + {\rm{f}}\left( {{\rm{x}}\left( {\rm{t}} \right){\rm{\dot x}}\left( {\rm{t}} \right)} \right) + {\rm{g}}\left( {{\rm{x}}\left( {{\rm{t}} - {\rm{r}}} \right)} \right) = 0$$ -- 32. The “Adjoint” Equation for General Linear Systems -- 33. The True Adjoint of a Linear System -- 34. Boundary Value Problems -- 35. Linear Periodic Systems. General Theory -- 36. Decomposition of Linear Periodic Systems -- 37. Nondegenerate Periodic Orbits -- 38. Notes and Remarks.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-1-4615-9968-5
Links to Related Works	Subject References: Analysis . Analysis (Mathematics) . Mathematical analysis . Mathematics . Authors: Hale, Jack K. . Corporate Authors: SpringerLink (Online service) . Series: Applied mathematical sciences . Classification: 515 .

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Functional Differential Equations

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