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Functional Equations with Causal Operators [Kõva köide]

(University of Texas at Arlington, USA)
Teised raamatud teemal:
Functional Equations with Causal OperatorsSuurem pilt
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Püsilink: https://www.kriso.ee/db/9780415271868.html
Märksõnad:
Functional equations encompass most of the equations used in applied science and engineering: ordinary differential equations, integral equations of the Volterra type, equations with delayed argument, and integro-differential equations of the Volterra type. The basic theory of functional equations includes functional differential equations with causal operators. Functional Equations with Causal Operators explains the connection between equations with causal operators and the classical types of functional equations encountered by mathematicians and engineers. It details the fundamentals of linear equations and stability theory and provides several applications and examples.
Introduction to the Series vii
Preface ix
Introduction
1(9)
Classes of Functional Equations
1(3)
Equations with Causal Operators
4(3)
Causal Operators in Applications
7(3)
Auxiliary concepts
10(21)
Abstract Spaces
10(6)
Function Spaces
16(6)
Operators on Function Spaces
22(6)
Fixed Points and Other Auxilary Results
28(3)
Existence theory for Functional equations with causal operators
31(48)
The Equation x(t) = (Vx)(t) in the Space of Continuous Functions
31(6)
The Equation x(t) = (Vx)(t) in Spaces of Measurable Functions
37(6)
Existence and Approximations of Solution by Means of the Singular Perturbation Technique
43(3)
Global Existence Results for Functional Equations with Causal Operators
46(10)
Some Global Results of Existence and Uniqueness
56(9)
Functional Inequalities
65(6)
Initial Value Problems of the Second Kind for Functional Differential Equations
71(8)
Linear and quasilinear equations with causal operators
79(22)
Global Existence and Uniqueness for Linear Functional Differntial Equations
79(2)
Global Existence and Uniqueness for Linear Functional Equations
81(3)
Integral Representation of Solutions of Linear Functional Differential Equations
84(5)
Initial Value Problems with Functional Data for Linear Functional Differential Equations
89(3)
Quasilinear Functional Equations
92(6)
Two-Point Boundary Value Problems
98(2)
Comments and References
100(1)
Stability theory
101(22)
Definition and Generalities
101(2)
Stability of Linear Systems
103(7)
Stability of Quasilinear Systems
110(4)
Comparison Method in Stability
114(5)
Admissibility Concepts
119(4)
Neutral functional equations
123(14)
The Concept of Neutral Functional Equation with Causal Operators
123(1)
Existence Results in the Continuous Case
124(5)
Existence Results in Spaces of Measurable Functions
129(2)
More Results on Neutral Functional Differential Equations
131(3)
The Linear and Quasilinear Cases
134(3)
Miscellanea (applications and generalizations)
137(18)
A Linear-Quadratic Optimal Control Problem with Causal Operators
137(5)
A Maximum Principle Approach
142(2)
Asymptotic Behavior in Second-Order Systems
144(4)
Global Existence for the Equation x(t) = (Lx)(t) + (Nx)(t)
148(2)
Review of Further Results and Topics
150(5)
Appendix 155(5)
References 160(7)
Index 167


C. Corduneanu