Method of Averaging for Differential Equations on an Infinite Interval: Theory and Applications (Lecture Notes in Pure and Applied Mathematics Book 255)

In recent years, mathematicians have detailed simpler proofs of known theorems, have identified new applications of the method of averaging, and have obtained many new results of these applications. Encompassing these novel aspects, Method of Averaging of the Infinite Interval: Theory and Applications rigorously explains the modern theory of the method of averaging and provides a solid understanding of the results obtained when applying this theory. The book starts with the less complicated theory of averaging linear differential equations (LDEs), focusing on almost periodic functions. It describes stability theory and Shtokalo's method, and examines various applications, including parametric resonance and the construction of asymptotics. After establishing this foundation, the author goes on to explore nonlinear equations. He studies standard form systems in which the right-hand side of a system is proportional to a small parameter and proves theorems similar to Banfi's theorem. The final chapters are devoted to systems with a rapidly rotating phase. Covering an important asymptotic method of differential equations, this book provides a thorough understanding of the method of averaging theory and its resulting applications. PREFACEAVERAGING OF LINEAR DIFFERENTIAL EQUATIONS Periodic and Almost Periodic Functions. Brief Introduction Bounded Solutions Lemmas on Regularity and Stability Parametric Resonance in Linear Systems Higher Approximations. Shtokalo Method Linear Differential Equations with Fast and Slow Time Asymptotic Integration Singularly Perturbed Equations AVERAGING OF NONLINEAR SYSTEMS Systems in Standard Form. First ApproximationSystems in Standard Form. First ExamplesPendulum Systems with an Oscillating Pivot Higher Approximations of the Method of AveragingAveraging and StabilitySystems with a Rapidly Rotating Phase Systems with a Fast Phase. Resonant Periodic Oscillations Systems with Slowly Varying ParametersAPPENDICES Almost Periodic Functions Stability of the Solutions of Differential Equations Some Elementary Facts from the Functional AnalysisREFERENCESINDEX "In recent years, mathematicians have detailed simpler proofs of known theorems, have identified new applications of the method of averaging, and have obtained many new results of these applications. Encompassing these novel aspects, Method of Averaging for Differential Equations on an Infinite Interval: Theory and Applications rigorously explains the modern theory of the method of averaging and provides a solid understanding of the results obtained when applying this theory."--BOOK JACKET Explains the modern theory of the method of averaging and provides a understanding of the results obtained when applying this theory. This book starts with the less complicated theory of averaging linear differential equations (LDEs), focusing on almost periodic functions. It also includes chapters devoted to systems with a rapidly rotating phase