Ordinary Differential Equations in Rn : Problems and Methods

✍ Scribed by L. C. Piccinini, G. Stampacchia, G. Vidossich (auth.)

• Publisher: Springer-Verlag New York
• Year: 1984
• Tongue: English
• Leaves: 395
• Series: Applied Mathematical Sciences 39
• Edition: 1
• Category: Library

✦ Synopsis

During the fifties, one of the authors, G. Stampacchia, had prepared some lecture notes on ordinary differential equations for a course in ad­ analysis. These remained for a long time unused because he was no vanced longer very interested in the study of such equations. We now see, though, that numerous applications to biology, chemistry, economics, and medicine have recently been added to the traditional ones in mechanics; also, there has been in these last years a reemergence of interest in nonlinear analy­ sis, of which the theory of ordinary differential euqations is one of the principal sources of methods and problems. Hence the idea to write a book. Our text, based on the old notes and experience gained in many courses, seminars, and conferences, both in Italy and abroad, aims to give a simple and rapid introduction to the various themes, problems, and methods of the theory of ordinary differential equations. The book has been conceived in such a way so that even the reader who has merely had a first course in calculus may be able to study it and to obtain a panoramic vision of the theory. We have tried to avoid abstract formalism, preferring instead a discursive style, which should make the book accessible to engineers and physicists without specific preparation in modern mathematics. For students of mathematics, it pro­ vides motivation for the subject of more advanced analysis courses.

✦ Table of Contents

Front Matter....Pages i-xii
Existence and Uniqueness for the Initial Value Problem Under the Hypothesis of Lipschitz....Pages 1-78
Linear Systems....Pages 79-131
Existence and Uniqueness for the Cauchy Problem Under the Condition of Continuity....Pages 132-206
Boundary Value Problems....Pages 207-310
Questions of Stability....Pages 311-381
Back Matter....Pages 382-385

✦ Subjects

Analysis