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Advanced Functional Evolution Equations and Inclusions 2015 ed. [Kõva köide]

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  • Formaat: Hardback, 408 pages, kõrgus x laius: 235x155 mm, kaal: 7686 g, XXI, 408 p., 1 Hardback
  • Sari: Developments in Mathematics 39
  • Ilmumisaeg: 13-Jul-2015
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 3319177672
  • ISBN-13: 9783319177670
Teised raamatud teemal:
Advanced Functional Evolution Equations and Inclusions 2015 ed.Suurem pilt
  • Formaat: Hardback, 408 pages, kõrgus x laius: 235x155 mm, kaal: 7686 g, XXI, 408 p., 1 Hardback
  • Sari: Developments in Mathematics 39
  • Ilmumisaeg: 13-Jul-2015
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 3319177672
  • ISBN-13: 9783319177670
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9783319177670.html
Märksõnad:
This book presents up-to-date results on abstract evolution equations and differential inclusions in infinite dimensional spaces. It covers equations with time delay and with impulses, and complements the existing literature in functional differential equations and inclusions. The exposition is devoted to both local and global mild solutions for some classes of functional differential evolution equations and inclusions, and other densely and non-densely defined functional differential equations and inclusions in separable Banach spaces or in Fréchet spaces. The tools used include classical fixed points theorems and the measure-of non-compactness, and each chapter concludes with a section devoted to notes and bibliographical remarks.This monograph is particularly useful for researchers and graduate students studying pure and applied mathematics, engineering, biology and all other applied sciences.

1. Preliminary Background.- 2. Partial Functional Evolution Equations with Finite Delay.- 3. Partial Functional Evolution Equations with Infinite Delay.- 4. Perturbed Partial Functional Evolution Equations.- 5. Partial Functional Evolution Inclusions with Finite Delay.- 6. Partial Functional Evolution Inclusions with Infinite Delay.- 7. Densely Defined Functional Differential Inclusions with Finite Delay.- 8. Non-Densely Defined Functional Differential Inclusions with Finite Delay.- 9. Impulsive Semi-linear Functional Differential Equations.- 10. Impulsive Functional Differential Inclusions with Unbounded Delay.- 11. Functional Differential Inclusions with Multi-valued Jumps.- 12. Global Existence Results for Functional Differential Equations and Inclusions with Delay.- 13. Global Existence Results of Second Order Functional Differential Equations with Delay.- References.- Index.

Arvustused

In this monograph, the authors present their results on various partial functional and neutral functional differential equations and inclusions in infinite dimensional spaces obtained in the last years. The book is organized in 13 chapters, an extensive bibliography and an index. This book will be useful to researchers and graduate students interested in functional evolution equations and inclusions. (Rodica Luca, zbMATH, Vol. 1326.34012, 2016)

1 Preliminary Background
1(16)
1.1 Notations and Definitions
1(1)
1.2 Some Properties in Frechet Spaces
2(1)
1.3 Phase Spaces
3(2)
1.4 Set-Valued Maps
5(2)
1.5 Evolution System
7(1)
1.6 Semigroups
7(3)
1.6.1 C0-Semigroups
7(2)
1.6.2 Integrated Semigroups
9(1)
1.6.3 Extrapolated Semigroups
10(1)
1.7 Some Fixed Point Theorems
10(7)
2 Partial Functional Evolution Equations with Finite Delay
17(30)
2.1 Introduction
17(1)
2.2 Partial Functional Evolution Equations
17(7)
2.2.1 Introduction
17(1)
2.2.2 Main Result
18(3)
2.2.3 An Example
21(1)
2.2.4 Nonlocal Case
22(2)
2.3 Neutral Functional Evolution Equations
24(8)
2.3.1 Introduction
24(1)
2.3.2 Main Result
24(5)
2.3.3 An Example
29(1)
2.3.4 Nonlocal Case
30(2)
2.4 Partial Functional Integro-Differential Evolution Equations
32(6)
2.4.1 Introduction
32(1)
2.4.2 Main Result
32(4)
2.4.3 An Example
36(1)
2.4.4 Nonlocal Case
37(1)
2.5 Neutral Functional Integro-Differential Evolution Equations
38(7)
2.5.1 Introduction
38(1)
2.5.2 Main Result
38(4)
2.5.3 An Example
42(2)
2.5.4 Nonlocal Case
44(1)
2.6 Notes and Remarks
45(2)
3 Partial Functional Evolution Equations with Infinite Delay
47(46)
3.1 Introduction
47(1)
3.2 Partial Functional Evolution Equations
47(6)
3.2.1 Introduction
47(1)
3.2.2 Existence and Uniqueness of Mild Solution
48(4)
3.2.3 An Example
52(1)
3.3 Controllability on Finite Interval for Partial Evolution Equations
53(9)
3.3.1 Introduction
53(1)
3.3.2 Controllability of Mild Solutions
54(7)
3.3.3 An Example
61(1)
3.4 Controllability on Semi-infinite Interval for Partial Evolution Equations
62(6)
3.4.1 Introduction
62(1)
3.4.2 Controllability of Mild Solutions
63(4)
3.4.3 An Example
67(1)
3.5 Neutral Functional Evolution Equations
68(7)
3.5.1 Introduction
68(1)
3.5.2 Existence and Uniqueness of Mild Solution
69(5)
3.5.3 An Example
74(1)
3.6 Controllability on Finite Interval for Neutral Evolution Equations
75(9)
3.6.1 Introduction
75(1)
3.6.2 Controllability of Mild Solutions
76(6)
3.6.3 An Example
82(2)
3.7 Controllability on Semi-infinite Interval for Neutral Evolution Equations
84(8)
3.7.1 Introduction
84(1)
3.7.2 Controllability of Mild Solutions
84(7)
3.7.3 An Example
91(1)
3.8 Notes and Remarks
92(1)
4 Perturbed Partial Functional Evolution Equations
93(20)
4.1 Introduction
93(1)
4.2 Perturbed Partial Functional Evolution Equations with Finite Delay
93(7)
4.2.1 Introduction
93(1)
4.2.2 Existence of Mild Solutions
94(5)
4.2.3 An Example
99(1)
4.3 Perturbed Neutral Functional Evolution Equations with Finite Delay
100(6)
4.3.1 Introduction
100(1)
4.3.2 Existence of Mild Solutions
100(5)
4.3.3 An Example
105(1)
4.4 Perturbed Partial Functional Evolution Equations with Infinite Delay
106(6)
4.4.1 Introduction
106(1)
4.4.2 Existence of Mild Solutions
106(5)
4.4.3 An Example
111(1)
4.5 Notes and Remarks
112(1)
5 Partial Functional Evolution Inclusions with Finite Delay
113(14)
5.1 Introduction
113(1)
5.2 Partial Functional Evolution Inclusions
113(6)
5.2.1 Introduction
113(1)
5.2.2 Existence of Mild Solutions
114(4)
5.2.3 An Example
118(1)
5.3 Neutral Functional Evolution Inclusions
119(7)
5.3.1 Introduction
119(1)
5.3.2 Existence of Mild Solutions
120(4)
5.3.3 An Example
124(2)
5.4 Notes and Remarks
126(1)
6 Partial Functional Evolution Inclusions with Infinite Delay
127(16)
6.1 Introduction
127(1)
6.2 Partial Functional Evolution Inclusions
127(8)
6.2.1 Introduction
127(1)
6.2.2 Existence of Mild Solutions
128(5)
6.2.3 An Example
133(2)
6.3 Neutral Functional Evolution Inclusions
135(7)
6.3.1 Introduction
135(1)
6.3.2 Existence of Mild Solutions
135(6)
6.3.3 An Example
141(1)
6.4 Notes and Remarks
142(1)
7 Densely Defined Functional Differential Inclusions with Finite Delay
143(22)
7.1 Introduction
143(1)
7.2 Existence of Mild Solutions with Local Conditions
143(12)
7.2.1 Introduction
143(1)
7.2.2 Main Result
144(9)
7.2.3 Existence of Extremal Mild Solutions
153(2)
7.3 Existence of Mild Solutions with Nonlocal Conditions
155(1)
7.3.1 Main Result
155(1)
7.4 Application to the Control Theory
156(7)
7.4.1 Main Result
156(6)
7.4.2 Example
162(1)
7.5 Notes and Remarks
163(2)
8 Non-densely Defined Functional Differential Inclusions with Finite Delay
165(26)
8.1 Introduction
165(1)
8.2 Integral Solutions of Non-densely Defined Functional Differential Inclusions with Local Conditions
165(14)
8.2.1 Main Results
166(13)
8.3 Extremal Integral Solutions with Local Conditions
179(1)
8.4 Integral Solutions with Nonlocal Conditions
180(2)
8.4.1 Main Result
181(1)
8.5 Application to the Control Theory
182(7)
8.5.1 Main Result
183(4)
8.5.2 An Example
187(2)
8.6 Notes and Remarks
189(2)
9 Impulsive Semi-linear Functional Differential Equations
191(70)
9.1 Introduction
191(1)
9.2 Semi-linear Differential Evolution Equations with Impulses and Delay
191(12)
9.2.1 Introduction
191(1)
9.2.2 Existence of Mild Solutions
192(7)
9.2.3 Existence of Extremal Mild Solutions
199(1)
9.2.4 Impulsive Differential Equations with Nonlocal Conditions
200(1)
9.2.5 An Example
201(2)
9.3 Impulsive Semi-linear Functional Differential Equations with Non-densely Defined Operators
203(22)
9.3.1 Introduction
203(1)
9.3.2 Examples of Operators with Non-dense Domain
204(1)
9.3.3 Existence of Integral Solutions
205(10)
9.3.4 Existence of Extremal Integral Solutions
215(1)
9.3.5 Impulsive Differential Equations with Nonlocal Conditions
216(2)
9.3.6 Applications to Control Theory
218(5)
9.3.7 An Example
223(2)
9.4 Impulsive Semi-linear Neutral Functional Differential Equations with Infinite Delay
225(20)
9.4.1 Introduction
225(1)
9.4.2 Existence of Mild Solutions
226(8)
9.4.3 Existence of Integral Solutions
234(9)
9.4.4 An Example
243(2)
9.5 Non-densely Defined Impulsive Semi-linear Functional Differential Equations with State-Dependent Delay
245(14)
9.5.1 Introduction
245(1)
9.5.2 Existence of Integral Solutions
246(13)
9.6 Notes and Remarks
259(2)
10 Impulsive Functional Differential Inclusions with Unbounded Delay
261(44)
10.1 Introduction
261(1)
10.2 Densely Defined Impulsive Functional Differential Inclusions
261(17)
10.2.1 Introduction
261(2)
10.2.2 Mild Solutions
263(11)
10.2.3 Extremal Mild Solutions
274(2)
10.2.4 Example
276(2)
10.3 Non-densely Defined Impulsive Neutral Functional Differential Inclusions
278(15)
10.3.1 Mild Solutions
279(10)
10.3.2 Extremal Mild Solutions
289(2)
10.3.3 Example
291(2)
10.4 Controllability of Impulsive Semi-linear Differential Inclusions in Frechet Spaces
293(11)
10.4.1 Main Result
293(10)
10.4.2 Example
303(1)
10.5 Notes and Remarks
304(1)
11 Functional Differential Inclusions with Multi-valued Jumps
305(48)
11.1 Introduction
305(1)
11.2 Semi-linear Functional Differential Inclusions with State-Dependent Delay and Multi-valued Jump
305(12)
11.2.1 Introduction
305(1)
11.2.2 Existence of Integral Solutions
306(1)
11.2.3 Main Results
306(10)
11.2.4 Example
316(1)
11.3 Impulsive Evolution Inclusions with Infinite Delay and Multi-valued Jumps
317(7)
11.3.1 Introduction
317(1)
11.3.2 Existence Results
318(5)
11.3.3 An Example
323(1)
11.4 Impulsive Semi-linear Differential Evolution Inclusions with Non-convex Right-Hand Side
324(6)
11.4.1 Introduction
324(1)
11.4.2 Existence Results
325(4)
11.4.3 An Example
329(1)
11.5 Impulsive Evolution Inclusions with State-Dependent Delay and Multi-valued Jumps
330(12)
11.5.1 Introduction
330(1)
11.5.2 Existence Results for the Convex Case
331(6)
11.5.3 Existence Results for the Non-convex Case
337(4)
11.5.4 An Example
341(1)
11.6 Controllability of Impulsive Differential Evolution Inclusions with Infinite Delay
342(10)
11.6.1 Introduction
342(1)
11.6.2 Existence and Controllability Results
343(8)
11.6.3 An Example
351(1)
11.7 Notes and Remarks
352(1)
12 Functional Differential Equations and Inclusions with Delay
353(32)
12.1 Introduction
353(1)
12.2 Global Existence for Functional Differential Equations with State-Dependent Delay
353(8)
12.2.1 Introduction
353(1)
12.2.2 Existence of Mild Solutions
354(5)
12.2.3 An Example
359(2)
12.3 Global Existence Results for Neutral Functional Differential Equations with State-Dependent Delay
361(8)
12.3.1 Introduction
361(1)
12.3.2 Existence of Mild Solutions
361(7)
12.3.3 An Example
368(1)
12.4 Global Existence Results for Functional Differential Inclusions with Delay
369(6)
12.4.1 Introduction
369(1)
12.4.2 Existence of Mild Solutions
370(4)
12.4.3 An Example
374(1)
12.5 Global Existence Results for Functional Differential Inclusions with State-Dependent Delay
375(8)
12.5.1 Introduction
375(1)
12.5.2 Existence of Mild Solutions
376(6)
12.5.3 An Example
382(1)
12.6 Notes and Remarks
383(2)
13 Second Order Functional Differential Equations with Delay
385(14)
13.1 Introduction
385(1)
13.2 Global Existence Results of Second Order Functional Differential Equations with Delay
385(12)
13.2.1 Introduction
385(1)
13.2.2 Existing Result for the Finite Delay Case
386(3)
13.2.3 Existing Results for the State-Dependent Delay Case
389(6)
13.2.4 Examples
395(2)
13.3 Notes and Remarks
397(2)
References 399(8)
Index 407