Ordinary Differential Equations and Boundary Value Problems Volume I: Advanced Ordinary Differential Equations
Authors : John R Graef (University of Tennessee at Chattanooga, USA), Johnny Henderson (Baylor University, USA), Lingju Kong (University of Tennessee at Chattanooga, USA), Xueyan Sherry Liu (St. Jude Children's Research Hospital, USA)
Publisher : World Scientific
ISBN : 978-981-3236-45-5
The authors begin with a study of initial value problems for systems of differential equations including the Picard and Peano existence theorems. The continuability of solutions, their continuous dependence on initial conditions, and their continuous dependence with respect to parameters are presented in detail. This is followed by a discussion of the differentiability of solutions with respect to initial conditions and with respect to parameters. Comparison results and differential inequalities are included as well.
Linear systems of differential equations are treated in detail as is appropriate for a study of ODEs at this level. Just the right amount of basic properties of matrices are introduced to facilitate the observation of matrix systems and especially those with constant coefficients. Floquet theory for linear periodic systems is presented and used to analyze nonhomogeneous linear systems.
Stability theory of first order and vector linear systems are considered. The relationships between stability of solutions, uniform stability, asymptotic stability, uniformly asymptotic stability, and strong stability are examined and illustrated with examples as is the stability of vector linear systems. The book concludes with a chapter on perturbed systems of ODEs.
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