Vrabie I. Differential Equations: An Introduction to Basic Concepts, Results and Applications

World Scientific Publishing, 2004. — 420 p.The book is an entirely rewritten English version of the lecture notes of a course on Differential Equations I taught during the last twelve years at the Faculty of Mathematics of Al. I. Cuza University of Iaqi. These lecture notes were written in 1999 in Romanian. Their goal was to present in a unitary frame and from a new perspective the main concepts and results belonging to a discipline which, due t o the continuous interplay between theory and applications, is by far one of the most fascinating branches of modern mathematics, i.e. differential equations. It was my intention to give the reader the opportunity to know a point of view – rather different from the traditional one – offering a possible way to learn differential equations with main emphasis on the Cauchy problem. So, I decided to treat separately the problems o f existence, uniqueness, approximation, continuation of the solutions and, at the same time, to give the simplest possible but complete proofs to some fundamental results which are at the core of the discipline: Peano’s local existence theorem, the classification of non-continuable solutions from the viewpoint of their behavior at t he end of the existence interval, the continuous dependence of the solution on the data and parameters, etc.