Differential equations. An introduction to basic concepts, results and applications (Q5890765)

This is the 3rd edition of a remarkably comprehensive textbook in differential equations. Writing a textbook in this field is not an easy job. Since the 50ies of the previous century it has been pointed out that writing a book on ordinary differential equations is somehow a problem of personal taste. The author, an outstanding representative of the Iaşi (Romania) school of ordinary and partial differential equations, has focused in his book on those topics he knew better but also on those his teaching experience considered as representative. Consequently, taking into account the success of the first edition of 2004 [Zbl 1070.34001], the author augmented the book by new chapters -- relevant for both research and teaching. For instance, the 2nd edition was augmented by two chapters: Volterra equations (which nevertheless belongs to a standard course on ``Differential and integral equations'') -- viewed as a good starting point for Operator Theory/Functional Analysis -- and Calculus of variations (usually included in a course of Mathematical Physics) -- possibly in connection with Optimization Theory. An interesting feature of the 2nd edition was the introduction of the Laplace transform. Usually the Laplace transform is avoided in the curricula of Mathematics while being basic in Electrical/ Mechanical Engineering for studying transients (described by ordinary differential as well as by Volterra equations, sometimes even by partial differential equations of hyperbolic or parabolic type).NEWLINENEWLINEThe 3d edition is also augmented by two such new chapters: on Nonlocal problems and on Delay functional differential equations. The Chapter on nonlocal problems (Chapter 10) deals with ``nonlocal'' initial conditions e.g. \(x(0)=g(x(\cdot))\) with \(x(\cdot)\) some future state. For the solutions of such problems, existence, uniqueness and global stability are discussed. For the delay functional differential equations (Chapter 11) there are considered local and global existence; these equations are illustrated by two applications from Physics and Biotechnology. We consider remarkable this fact of including the functional differential equations in a textbook on ordinary differential equations. Due to its structure and applications/exercises parts, the book is highly recommended for both undergraduate and graduate studies. Researchers and faculty will also find this book interesting and useful.