Multivalued Differential Equations

Bìa trước
Walter de Gruyter, 22 thg 7, 2011 - 271 trang

The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear analysis and applications in various fields, such as optimization, control theory, systems theory, mechanics, engineering, and other sciences. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of nonlinear analysis. Contributions which are on the borderline of nonlinear analysis and related fields and which stimulate further research at the crossroads of these areas are particularly welcome.

Please submit book proposals to Jürgen Appell.

 

Các trang được chọn

Nội dung

Multis
1
1 Upper Semicontinuity
3
12 Upper Semicontinuity
4
13 Properties of Use Multis
6
14 Other Tests for Usc
8
Problems
9
2 Lower Semicontinuity
12
22 Continuous Selections
13
84 Related Problems
98
85 Gronwalls Lemma
100
86 Convexification
102
87 Remarks
105
Existence Theory in Infinite Dimensions
109
9 Compactness Conditions
111
92 Measures of Noncompactness
113
93 The Usc Case
115

23 Continuity
15
24 Locally Lipschitz Approximations of Usc Multis
16
25 Remarks
17
Problems
18
3 Measurability
21
32 Measurable Selections
22
33 Approximation by StepMultis
23
34 Some Consequences
25
35 Multis of Two Variables
26
36 Remarks
27
Problems
28
4 Mishmash
31
42 Bochner Integrals
34
43 Monotone Multis
35
44 Accretive Multis
38
45 Some Basic Facts about Banach Spaces
42
46 Remarks
43
Problems
44
Existence Theory in Finite Dimensions
49
5 Upper Semicontinuous RightHand Sides
52
51 The Usc Case
53
52 CounterExamples
54
53 The Carathéodory Case
56
54 Some Consequences
58
55 Remarks
60
Problems
61
6 Lower Semicontinuous RightHand Sides
65
61 The Lsc Case
66
62 The Carathéodory Case
68
63 Some Consequences
71
64 Remarks
74
Problems
75
Solution Sets
77
7 Topological Properties of Solution Sets
79
72 Invariance
80
73 Connectedness in the Usc Case
81
74 Connectedness in the Lsc Case
84
76 Remarks
85
Problems
87
8 Comparison of Solutions
91
82 Extremal Solutions I
92
83 Extremal Solutions II
95
94 The Lsc Case
119
95 Remarks
124
Problems
125
10 Noncompactness Conditions
130
102 Extreme Points
131
103 Proof of Theorem 101
133
104 Lipschitz Conditions
135
105 Monotonicity
136
106 Hyperaccretivity
140
107 Remarks
141
Problems
142
Fixed Points and Qualitative Theory
143
11 Fixed Points
146
112 Weakly Inward Maps
149
113 SetContractions
151
114 Degree Theory
154
115 An Example
156
116 Remarks
158
Problems
160
12 Boundary Value Problems
164
122 SturmLiouville Problems
167
123 Solutions in Closed Sets
173
124 Remarks
177
Problems
178
13 Periodic Solutions
181
132 Another Fixed Point Problem
182
133 Examples
186
134 Remarks
197
14 Stability and Asymptotic Behavior
202
142 Stability Tests
204
143 Asymptotic Behavior
208
144 Perturbations
213
145 Remarks
217
Problems
222
Related Topics
227
A 2 Implicit Differential Equations
233
A 3 Functional Differential Equations
235
A 4 Perturbations of Dissipative RightHand Sides
237
References
243
Index
259
Bản quyền

Ấn bản in khác - Xem tất cả

Multivalued Differential Equations
Klaus Deimling
Xem trước bị giới hạn - 1992

Thuật ngữ và cụm từ thông dụng

a.c. solution arcwise connected assume assumptions asymptotically stable bounded sets c₁ Carathéodory closed bounded convex closed convex values closed graph closed values compact convex values compact values condition consider continuous selection conv F conv F(t convex set Corollary Cx(J D₁ defined Deimling Example exists ɛ-d-usc F is usc F(wo F₁ F₂ Fix(F fixed point Fo(t functions given graph(F hence Hilbert space Hint implies initial value problem L¹(J Lebesgue measurable linear Lipschitz locally Lipschitz measurable selection measurable space minimal solution monotone multi multivalued notice obvious partition of unity properties Proposition real Banach space Remark result right-hand side single-valued solution set strongly measurable subsets T₂(x Theorem 5.2 uniformly convex usc with compact w-periodic solution x₁ y₁ Y₂ yields Zorn's Lemma

Thông tin thư mục

Tiêu đềMultivalued Differential Equations
Tập 1 trong tổng số De Gruyter Series in Nonlinear Analysis and Applications
Tác giảKlaus Deimling
Ấn bảnin lại
Nhà xuất bảnWalter de Gruyter, 2011
ISBN3110874229, 9783110874228
Độ dài271 trang
  
Xuất lời trích dẫnBiBTeX EndNote RefMan