Introduction to The Theory of Functional Differential Equations: Methods and Applications (Contemporary Mathematics and Its Applications Book Series)

Preface......Page 8
1.1. Preliminary knowledge from the theory of linear equations in Banach spaces......Page 12
1.2. Linear equation and linear boundary value problem......Page 17
1.3. The Green operator......Page 23
1.4. Problems lacking the everywhere and unique solvability......Page 31
1.5. Continuous dependence on parameters......Page 40
2.1. Introduction......Page 52
2.2. Equations in the space of absolutely continuous functions......Page 53
2.3. Equations of the nth order......Page 70
2.4. Equations in spaces of functions defined on the semiaxis......Page 87
2.5. Equations with generalized Volterra operators......Page 101
3.1. Introduction......Page 110
3.2. Equations in the space of piecewise absolutely continuous functions......Page 111
3.3. Equations of the nth order with impulse effect......Page 119
3.4. Multipoint boundary value problem for the Poisson equation......Page 126
4.1. Introduction......Page 132
4.2. The equation (t-a)(b-t)(t)-(Tx)(t)= f(t)......Page 133
4.3. Inner singularities......Page 148
4.4. The chemical reactor's equation......Page 153
5.2. The criterion for the existence of the minimum of the square functional......Page 160
5.3. The tests of the existence of the minimum of the functional......Page 168
6.1. Introduction......Page 184
6.2. General theorem on the solvability of the boundary value problem......Page 185
6.3. BVP in the space of absolutely continuous functions......Page 188
6.4. BVP in the space of piecewise absolutely continuous functions......Page 202
6.5. Boundary value problem for a singular equation......Page 204
6.6. The Cauchy matrix and a posteriori error bounds......Page 210
6.7. Other applications of the constructive approach......Page 214
7.1. Introduction......Page 224
7.2. Equations with monotone operators......Page 225
7.3. Reducibility of equations......Page 235
7.4. A priori inequalities......Page 247
7.5. Nonlinear boundary value problems......Page 258
7.6. Sufficient conditions for minimum of functionals......Page 262
7.7. Reducible stochastic functional differential equations......Page 275
A. On the spectral radius estimate of a linear operator......Page 292
B. A compactness condition for a linear integral operator in the space of summable functions......Page 295
C. The composition operator......Page 296
D. Vallee-Poussin-like theorem......Page 307
Bibliography......Page 313
BookmarkTitle:......Page 314