Asymptotically Almost Periodic Solutions of Differential Equations

Preface......Page 6
Notation......Page 12
Contents......Page 8
1.1. Some Notions and Denotations......Page 18
1.2. Poisson Asymptotically Stable Motions......Page 21
1.3. Criterion of Asymptotical Almost Periodicity......Page 23
1.4. Asymptotically Periodic Motions......Page 27
1.5. Asymptotically Almost Periodic Functions......Page 30
1.6. Asymptotically Sp Almost Periodic Functions......Page 39
2.1. Comparability of Motions by the Character of Recurrence......Page 44
2.2. Comparability in Limit of Asymptotically Poisson Stable Motions......Page 47
2.3. Asymptotically Poisson Stable Solutions......Page 48
2.4. Asymptotically Periodic Solutions......Page 53
2.5. Homoclinic and Heteroclinic Motions......Page 54
2.6. Asymptotically Almost Periodic Systems with Convergence......Page 57
2.7. Some Tests of Convergence......Page 61
3.1. Some Nonautonomous Dynamical Systems......Page 66
3.2. Compatible in Limit Solutions......Page 68
3.3. Linear Differential Equations......Page 71
3.4. Semilinear Differential Equations......Page 109
3.5. Averaging Principle on Semiaxis for Asymptotically Almost Periodic Equations......Page 113
3.6. Nonlinear Differential Equations......Page 115
3.7. Bilaterally Asymptotically Almost Periodic Solutions......Page 119
3.8. Asymptotically Almost Periodic Equations with Convergence......Page 127
4.1. Bounded on Semiaxis Distributions......Page 134
4.2. Asymptotically Almost Periodic Distributions......Page 137
4.3. Asymptotically Almost Periodic Solutions of Linear Differential Equations with Distribution Perturbations......Page 140
4.4. Asymptotically Almost Periodic Distributions......Page 142
4.5. Solvability of the Equation x'=A(t)x+f(t) in the Class of AsymptoticallyAlmost Periodic Distributions AP'm (R+)......Page 144
4.6. Dynamical Systems of Shifts in the Spaces of Distributions and Asymptotically Almost Periodic Functions in the Sobolev Spaces......Page 148
4.7. Weakly Asymptotically Almost Periodic Functions......Page 153
4.8. Linear and Semilinear Differential Equations with Weakly Asymptotically Almost Periodic Coefficients......Page 159
5.1. Functional Differential Equations (FDEs) and Dynamical Systems......Page 164
5.2. Asymptotically Almost Periodic Solutions of FDEs......Page 167
5.3. Linear FDEs......Page 168
5.4. Semilinear FDEs......Page 170
5.5. Integral Equations of Volterra and Generated by the NonautonomousDynamical Systems......Page 173
5.6. Asymptotically Almost Periodic Solutions for Integral Equations of Volterra......Page 176
5.7. Convergence of Some Evolution Equations......Page 179
Bibliography......Page 191
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