Theory of singular boundary value problems. (English) Zbl 0807.34028

O’Regan, Donal

Singapore: World Scientific. xi, 154 p. (1994).

This short monograph is devoted to the use of Leray-Schauder type continuation theorems to prove the existence of some regular and singular two-point boundary value problems for second order nonlinear ordinary differential equations. The cases of bounded and unbounded intervals are both considered. Although the book intends to survey some topics of current interest in this area, it is mostly devoted to gathering together some contributions of its author and his coworkers, after some introductory chapters on the foundations of fixed point theory, existence principles and linear operator theory.
Even if the author has made no attempt to give some of the results in their most general formulation, many statements are complicated enough to be more attractive to experts than to beginners. In addition, although a list of references is given after each chapter, one can regret that there is no direct connection to those references in the text itself. Hence the reader will have to do all the work in finding the original sources of the various contributions and trying to understand the source and the development of the underlying ideas.

Reviewer: J.Mawhin (Louvain-La-Neuve)

MSC:

34B15	Nonlinear boundary value problems for ordinary differential equations
34-02	Research exposition (monographs, survey articles) pertaining to ordinary differential equations
34-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to ordinary differential equations

Keywords:

Leray-Schauder type continuation theorems; singular two-point boundary value problems; second order nonlinear ordinary differential equations