Solvability of Nonlinear Singular Problems for Ordinary Differential Equations (Book Series: Contemporary Mathematics and Its Applications)

The topic of singular boundary value problems has been of substantial and rapidly growing interest for many scientists and engineers. This book is devoted to singular boundary value problems for ordinary differential equations. It presents existence theory for a variety of problems having unbounded nonlinearities in regions where their solutions are searched for. The importance of thorough investigation of analytical solvability is emphasized by the fact that numerical simulations of solutions to such problems usually break down near singular points. The book provides both general existence principles and effective existence criteria which give a theoretical framework for investigation of variety singular boundary value problems, such as Dirichlet, periodic, mixed, focal, conjugate, Sturm-Liouville, Lidstone, or nonlocal problems. The book is addressed to researchers in related areas, to graduate students or advanced undergraduates, and, in particular, to those interested in singular and nonlinear boundary value problems. It can serve as a reference book on the existence theory for singular boundary value problems of ordinary differential equations as well as a textbook for graduate or undergraduate classes. The content of the monograph is mainly based on results obtained by the authors during the last few years, and it also systematically describes the existing literature and compares various known existence results. The impact of the theoretical results is demonstrated by illustrative examples. The selection of topics reflects the particular interests of the authors.