Linear differential equations in Banach space

Cover......Page 1
Title......Page 2
Preface......Page 4
Table of Contents......Page 6
Introduction......Page 8
1. The Cauchy problem......Page 31
2. Uniformly correct Cauchy problem......Page 49
3. Weakened Cauchy problem......Page 66
4. Equations in Hilbert space......Page 89
5. Fractional powers of operators......Page 115
6. Nonhomogeneous equations......Page 136
7. Equations with perturbed operators......Page 150
8. Examples......Page 165
1. Unbounded operators depending on a parameter......Page 183
2. Equations with bounded operators......Page 195
3. The uniformly correct Cauchy problem , . .......Page 199
4. Weakened Cauchy problem .......Page 216
5. Abstract parabolic equations with operators having variable domains m......Page 235
1. The hyperbolic case. The Cauchy problem......Page 245
2. The elliptic case. Boundary problems......Page 256
3. The Cauchy problem for the complete equation of the second order......Page 277
1. Equations with a small parameter on the highest derivative......Page 290
2. Evolution of subspaces in Banach space......Page 304
3. Splitting of an equation into equations in subspaces......Page 316
1. Factor-method of solution of operator equations......Page 340
2. Finite-difference factor-method for evolution equations.......Page 347
Remarks and References to the Literature......Page 369
Bibliography......Page 384