Almost Periodic Oscillations and Waves (eBook)

 C. Corduneanu has published extensively: Integral Equations and Applications, HC, 1991, Cambridge Univ. Press, 978-0521340502, 376 pp. Functional Equations with Causal Operators (Stability and Control: Theory, Methods and Applications, 16)  (Kindle Edition), $119.95, Taylor & Francis, 2007 Functional Equations with Causal Operators (Stability and Control: Theory, Methods and Applications, 16)  (HC Edition), $119.95, CRC, 2002, 978-0415271868 with I. Sandberg, Volterra Equations and Applications (Stability and Control), $179.00, 512pp, CRC, 2000, 978-9056991715 The author is a renowned expert in the fields of ordinary and partial differential equations.

Preface 5
Contents 7
1 Introduction 9
2 Metric Spaces and Related Topics 22
2.1 Metric Spaces 22
2.2 Banach Spaces and Hilbert Spaces 27
2.3 Function Spaces: Continuous Case 35
2.4 Completion of Metric Spaces 40
2.5 Function Spaces: Measurable Case 45
3 Basic Properties of Almost Periodic Functions 56
3.1 The Space AP1(R, C) 56
3.2 The Space AP(R, C) 60
3.3 The Space S(R, C) 67
3.4 Besicovitch Spaces the Mean Value
3.5 The Space AP(R, X), X-Banach Space 78
3.6 Almost Periodic Functions Depending on Parameters 88
3.7 Variations on the Theme of Almost Periodicity 94
4 Fourier Analysis of Almost Periodic Functions 103
4.1 General Remarks 103
4.2 The Fourier Series Associated to an Almost Periodic Function 105
4.3 Convergence of Fourier Series 111
4.4 Summability of Fourier Series 117
4.5 The Fourier Series of Almost Periodic Functions in Banach Spaces 123
4.6 Further Topics Related to Fourier Series 132
5 Linear Oscillations 137
5.1 The Equation x.(t) = f(t) 137
5.2 Weakly Almost Periodic Functions 143
5.3 The Equation x.(t) = f(t) in Banach Spaces 150
5.4 Linear Oscillations Described by Ordinary Differential Equations 156
5.5 Linear Periodic and Almost Periodic Oscillations in Systems Described by Convolution Equations 162
5.6 Further Results on Almost Periodic Oscillations in Linear Time-Invariant Systems 171
5.7 Almost Periodic Oscillations in Linear Time-Varying Systems 184
6 Almost Periodic Nonlinear Oscillations 191
6.1 Quasilinear Systems 191
6.2 Separated Solutions: Amerio’s Theory 196
6.3 The Second-Order Equation of Nonlinear Oscillations (Li´enard’s Type) 202
6.4 Equations with Monotone Operators 207
6.5 Gradient Type Systems 214
6.6 Qualitative Differential Inequalities 224
6.7 Further Results on Nonlinear Almost Periodic Oscillations Perturbed Systems
6.8 Oscillations in Discrete Processes 236
6.9 Oscillations in Systems Governed by Integral Equations 245
7 Almost Periodic Waves 253
7.1 Some General Remarks 253
7.2 Periodic Solitary Waves in One-Dimensional Hyperbolic and Parabolic Structures 257
7.3 Almost Periodic Heat Waves 262
7.4 Almost Periodic Waves a Linear Case
7.5 Almost Periodic Waves a Mildly Nonlinear System
7.6 A Case with Data on Characteristics 286
7.7 Miscellanea 292
7.8 Quasi-periodic Waves 300
References 307
Index 312