Sur une série dans la théorie des équations différentielles linéaires du second ordre à coefficients périodiques PDF Download

Author: Aleksandr Mikhailovitch Liapounoff
Publisher:
ISBN:
Category :
Languages : fr
Pages :

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Author: Aleksandr Michajlovič Ljapunov
Publisher:
ISBN:
Category :
Languages : fr
Pages : 0

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Author: Aleksandr Michajlovič Ljapunov
Publisher:
ISBN:
Category :
Languages : fr
Pages : 70

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Author: Lamberto Cesari
Publisher: Springer
ISBN: 3662015293
Category : Mathematics
Languages : en
Pages : 278

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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 deepen 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, auto 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 view 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.

Author: A. F. Leont'Ev
Publisher: American Mathematical Soc.
ISBN: 9780821817100
Category :
Languages : en
Pages : 418

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Author: Royal Society (Great Britain)
Publisher:
ISBN:
Category : Learned institutions and societies
Languages : en
Pages : 1066

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Author: Aleksandr Mikhaĭlovitch Liapounov
Publisher:
ISBN:
Category :
Languages : fr
Pages : 70

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Author: Krein
Publisher: Birkhäuser
ISBN: 3034854161
Category : Science
Languages : en
Pages : 310

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In this volume three important papers of M.G. Krein appear for the first time in English translation. Each of them is a short self-contained monograph, each a masterpiece of exposition. Although two of them were written more than twenty years ago, the passage of time has not decreased their value. They are as fresh and vital as if they had been written only yesterday. These papers contain a wealth of ideas, and will serve as a source of stimulation and inspiration for experts and beginners alike. The first paper is dedicated to the theory of canonical linear differential equations, with periodic coefficients. It focuses on the study of linear Hamiltonian systems with bounded solutions which stay bounded under small perturbations of the system. The paper uses methods from operator theory in finite and infinite dimensional spaces and complex analysis. For an account of more recent literature which was generated by this paper see AMS Translations (2), Volume 93, 1970, pages 103-176 and Integral Equations and Operator Theory, Volume 5, Number 5, 1982, pages 718-757.

Author: Stanley Winkler
Publisher:
ISBN:
Category : Differential equations
Languages : en
Pages : 102

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Author: Wilhelm Magnus
Publisher: Courier Corporation
ISBN: 9780486495651
Category : Mathematics
Languages : en
Pages : 154

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This two-part treatment of Hill's equation encompasses the subject's most pertinent information, explaining both basic theory and numerous details, including elementary formulas, oscillatory solutions, intervals of stability and instability, discriminants, and coexistence. Particular attention is given to stability problems and the question of coexistence of periodic solutions. 1966 edition.