Ordinary differential equations in Rn: problems and methods / L. C. Piccinini, G. Stampacchia, G. Vidossich

Auteur: Piccinini, Livio Clemente (1943-) - AuteurCo-auteur: Stampacchia, Guido (1922-1978) - Auteur ; Vidossich, Giovanni - AuteurAuteur secondaire : Lo Bello, Anthony (1947-) - TraducteurType de document: MonographieCollection: Applied mathematical sciences ; 39Langue: anglaisPays: Etats UnisÉditeur: New York : Springer, 1984Description: 1 vol. (xii-385 p.) ; 24 cm ISBN: 0387907238 ; br. Note: The present book is an excellent rapid introduction to the various problems and methods of the theory of ordinary differential equations. Besides the classical material this book contains also some unusual questions among which we mention: maximal and minimal solutions, some special methods for the study of stability of nonlinear differential systems (asymptotic equivalence, Olech's method, the method of the logarithmic norm, invariant sets) as well as some applications in biology, chemistry and automatic control theory. So the book is useful not only for engineers and physicists but also for mathematicians who can find here motivation for further advanced studies. A great number of interesting exercises completes the theoretical material. The text is divided into five chapters as follows: Chapter I, Existence and uniqueness for the initial value problem under the hypotheses of Lipschitz; Chapter II, Linear systems; Chapter III, Existence and uniqueness for the Cauchy problem under the condition of continuity; Chapter IV, Boundary value problems; Chapter V, Questions of stability. Each chapter, except Chapter II, also contains some bibliographical notes which give us a panoramic view related to the subjects and methods discussed in that chapter. In conclusion, the present book is a very welcome addition to the mathematical literature. (Zentralblatt)Bibliographie: Bibliogr. Index. Sujets MSC: 34A34 Ordinary differential equations -- General theory -- Nonlinear equations and systems, general
34D20 Ordinary differential equations -- Stability theory -- Stability
34Exx Ordinary differential equations -- Asymptotic theory
34A12 Ordinary differential equations -- General theory -- Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions
34A30 Ordinary differential equations -- General theory -- Linear equations and systems, general
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The present book is an excellent rapid introduction to the various problems and methods of the theory of ordinary differential equations. Besides the classical material this book contains also some unusual questions among which we mention: maximal and minimal solutions, some special methods for the study of stability of nonlinear differential systems (asymptotic equivalence, Olech's method, the method of the logarithmic norm, invariant sets) as well as some applications in biology, chemistry and automatic control theory. So the book is useful not only for engineers and physicists but also for mathematicians who can find here motivation for further advanced studies. A great number of interesting exercises completes the theoretical material. The text is divided into five chapters as follows: Chapter I, Existence and uniqueness for the initial value problem under the hypotheses of Lipschitz; Chapter II, Linear systems; Chapter III, Existence and uniqueness for the Cauchy problem under the condition of continuity; Chapter IV, Boundary value problems; Chapter V, Questions of stability. Each chapter, except Chapter II, also contains some bibliographical notes which give us a panoramic view related to the subjects and methods discussed in that chapter. In conclusion, the present book is a very welcome addition to the mathematical literature. (Zentralblatt)

Bibliogr. Index

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