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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, 1971
Edition Third Edition
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Descript X, 274 p. online resource


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 matic 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. The body of research now accumulated is overwhelming, and many books and reports have appeared on one or another of the multiple aspects of the new line of research which some authors call" qualitative theory of differential equations". The purpose of the present volume is to present many of the viewยญ points and questions in a readable short report for which completeness is not claimed. The bibliographical notes in each section are intended to be a guide to more detailed expositions and to the original papers. Some traditional topics such as the Sturm comparison theory have been omitted. Also excluded were all those papers, dealing with special differential equations motivated by and intended for the applications


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. General 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 -- ยง9. Analytical-topological methods -- IV. Asymptotic developments -- ยง 10. Asymtotic developments in general

Mathematics Differential equations Mathematics Ordinary Differential Equations


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