Oscillations in Nonlinear Systems by J K Hale

Oscillations in Nonlinear Systems by J K Hale

By focusing on ordinary differential equations that contain a small parameter, this concise graduate-level introduction to the theory of nonlinear oscillations provides a unified approach to obtaining periodic solutions to nonautonomous and autonomous differential equations. It also indicates key relationships with other related procedures and probes the consequences of the methods of averaging and integral manifolds.
Part I of the text features introductory material, including discussions of matrices, linear systems of differential equations, and stability of solutions of nonlinear systems. Part I offers extensive treatment of periodic solutions, including the general theory for periodic solutions based on the work of Cesari-Halel-Gambill, with specific examples and applications of the theory. Part I covers various aspects of almost periodic solutions, including methods of averaging and the existence of integral manifolds. An indispensable resource for engineers and mathematicians with knowledge of elementary differential equations and matrices, this text is illuminated by numerous clear examples.
Dover (2015) republication of the edition originally published by McGraw-Hill, New York, in 1963, and reprinted by Dover Publications, Inc., in 1992.
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Jack K. has been a professor at Brown University for many years. Hale is a Georgia Institute of Technology Regents Professor Emeritus and the author of Dover's Ordinary Differential Equations.