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AuthorCesari, Lamberto. author
TitleAsymptotic Behavior and Stability Problems in Ordinary Differential Equations [electronic resource] / by Lamberto Cesari
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1963
Edition Second Edition
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Descript 36 illus. online resource


This second edition, which has become necessary within so short a time, presents no major changes. However new results in the line of work of the author and of J. K. HaIe have made it advisable to rewrite seetion (8.5). Also, some references to most recent work have been added. LAMBERTO CESARI University of Michigan June 1962 Ann Arbor Preface to the First Edition In the last few decades the theory of ordinary differential equations has grown rapidly under the action of forces which have been working both from within and without: from within, as a development and deepenยญ ing of the concepts and of the topological and analytical methods brought about by LYAPUNOV, POINCARE, BENDIXSON, and a few others at the turn of the century; from without, in the wake of the technological development, particularly in communications, servomechanisms, autoยญ matie controls, and electronics. The early research of the authors just mentioned lay in challenging problems of astronomy, but the line of thought thus produced found the most impressive applications in the new fields


I. The concept of stability and systems with constant coefficients -- ยง 1. Some remarks on the concept of stability -- ยง 2. Linear systems with constant coefficients -- II. Genes al linear systems -- ยง 3. Linear systems with variable coefficients -- ยง 4. Linear systems with periodic coefficients -- ยง 5. The second order linear differential equation and generalizations -- III. Nonlinear systems -- ยง 6. Some basic theorems on nonlinear systems and the first method of Lyapunov -- ยง 7. The second method of Lyapunov -- ยง 8. Analytical methods -- ยง 9. Analytic-topological methods -- IV. Asymptotic developments -- ยง 10. Asymptotic developments in general

Mathematics Difference equations Functional equations Differential equations Mathematics Ordinary Differential Equations Difference and Functional Equations


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