Approximation Procedures in Nonlinear Oscillation Theory

"The book is well written and provides a good view of the important contributions of the school of Krasnoselʹskiĭ in the theory of nonlinear oscillations." __Mathematical Reviews__ "Undoubtedly it [the book] will be useful to all specialists in nonlinear analysis as well as oscillation theory." __Zentralblatt für Mathematik__

The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear analysis and applications in various fields, such as optimization, control theory, systems theory, mechanics, engineering, and other sciences. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of nonlinear analysis. Contributions which are on the borderline of nonlinear analysis and related fields and which stimulate further research at the crossroads of these areas are particularly welcome.

Editor-in-Chief
Jürgen Appell, Würzburg, Germany

Honorary and Advisory Editors
Catherine Bandle, Basel, Switzerland
Alain Bensoussan, Richardson, Texas, USA
Avner Friedman, Columbus, Ohio, USA
Umberto Mosco, Worcester, Massachusetts, USA
Louis Nirenberg, New York, USA
Alfonso Vignoli, Rome, Italy

Editorial Board
Manuel del Pino, Santiago, Chile
Mikio Kato, Nagano, Japan
Wojciech Kryszewski, Toru?, Poland
Simeon Reich, Haifa, Israel

Please submit book proposals to Jürgen Appell.

Titles in planning include

Eduardo V. Teixeira, Free Boundary Problems: A Primer (2018)
Lucio Damascelli and Filomena Pacella, Morse Index of Solutions of Nonlinear Elliptic Equations (2019)
Rafael Ortega, Periodic Differential Equations in the Plane: A Topological Perspective (2019)
Cyril Tintarev, Profile Decompositions and Cocompactness: Functional-Analytic Theory of Concentration Compactness (2020)
Takashi Suzuki, Semilinear Elliptic Equations: Classical and Modern Theories (2021)

The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear analysis and applications in various fields, such as optimization, control theory, systems theory, mechanics, engineering, and other sciences. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of nonlinear analysis. Contributions which are on the borderline of nonlinear analysis and related fields and which stimulate further research at the crossroads of these areas are particularly welcome. Editor-in-ChiefJürgen Appell, Würzburg, Germany Honorary and Advisory EditorsCatherine Bandle, Basel, SwitzerlandAlain Bensoussan, Richardson, Texas, USAAvner Friedman, Columbus, Ohio, USAUmberto Mosco, Worcester, Massachusetts, USA Editorial BoardManuel del Pino, Bath, UK, and Santiago, ChileMikio Kato, Nagano, JapanWojciech Kryszewski, Toruń, PolandVicenţiu D. Rădulescu, Kraków, PolandSimeon Reich, Haifa, Israel Please submit book proposals to Jürgen Appell. Titles in planning include Ireneo Peral Alonso and Fernando Soria, Elliptic and Parabolic Equations Involving the Hardy–Leray Potential (2020)Cyril Tintarev, Profile Decompositions and Cocompactness: Functional-Analytic Theory of Concentration Compactness (2020)Takashi Suzuki, Semilinear Elliptic Equations: Classical and Modern Theories (2021) Preface Chapter I: Basic Concepts § 1 Equations for oscillatory systems § 2 The shift operator and first return function § 3 Integral and integrofunctional operators for periodic problem § 4 The harmonic balance method § 5 The method of mechanical quadratures § 6 The collocation method § 7 The method of finite differences § 8 Factor methods Chapter II: Existence theorems for oscillatory regimes § 1 Smooth manifolds and differential forms § 2 Degree of a mapping § 3 Rotation of vector fields § 4 Completely continuous vector fields § 5 Fixed point principles and solution of operator equations § 6 Forced oscillations in systems with weak nonlinearities § 7 Oscillations in systems with strong nonlinearities. Directing functions method Chapter III: Convergence of numerical procedures § 1 Projection methods § 2 Factor methods § 3 Convergence of the harmonic balance method and the collocation method in the problem of periodic oscillations § 4 Convergence of the method of mechanical quadratures § 5 Convergence of the method of finite differences § 6 Numerical procedures of approximate construction of oscillatory regimes in autonomous systems § 7 Affinity theory § 8 Effective convergence criteria for numerical procedures § 9 Effective estimates of the convergence rate for the harmonic balance method Notes on the References References Index Nikolai A. Bobylev, Yu. M. Burman, Sergey K. Korovin. Includes Bibliographical References.