Mathematical Surveys and Monographs 2005; 328 pp; softcover Volume: 121 ISBN10: 0821852671 ISBN13: 9780821852675 List Price: US$88 Member Price: US$70.40 Order Code: SURV/121.S
 In 1836 and 1837, Sturm and Liouville published a series of papers on second order linear ordinary differential operators, which began the subject now known as the SturmLiouville theory. In 1910, Hermann Weyl published an article which started the study of singular SturmLiouville problems. Since then, SturmLiouville theory has remained an intensely active field of research with many applications in mathematics and mathematical physics. The purpose of the present book is (a) to provide a modern survey of some of the basic properties of SturmLiouville theory and (b) to bring the reader to the forefront of research on some aspects of this theory. Prerequisites for using the book are a basic knowledge of advanced calculus and a rudimentary knowledge of Lebesgue integration and operator theory. The book has an extensive list of references and examples and numerous open problems. Examples include classical equations and functions associated with Bessel, Fourier, Heun, Ince, Jacobi, Jörgens, Latzko, Legendre, LittlewoodMcLeod, Mathieu, Meissner, and Morse; also included are examples associated with the harmonic oscillator and the hydrogen atom. Many special functions of applied mathematics and mathematical physics occur in these examples. This book offers a wellorganized viewpoint on some basic features of SturmLiouville theory. With many useful examples treated in detail, it will make a fine independent study text and is suitable for graduate students and researchers interested in differential equations. Readership Graduate students and research mathematicians interested in differential equations. Reviews "In summary, this monograph offers a wealth of information on SturmLiouville theory and is an ideal textbook for a course in this field, serves as an indispensible source for every researcher working in this area, is ideally suited for selfstudy due to its detailed proofs and comprehensive bibliography, and is recommended to any applied scientist who wants to use SturmLiouville theory."  Zentralblatt MATH "...this monograph is a valuable and important work, useful for all people interested in the theory of secondorder linear differential operators."  Mathematical Reviews Table of Contents Part 1. Existence and uniqueness problems  First order systems
 Scalar initial value problems
Part 2. Regular boundary value problems  Twopoint regular boundary value problems
 Regular selfadjoint problems
 Regular leftdefinite and indefinite problems
Part 3. Oscillation and singular existence problems  Oscillation
 The limitpoint, limitcircle dichotomy
 Singular initial value problems
Part 4. Singular boundary value problems  Twopoint singular boundary value problems
 Singular selfadjoint problems
 Singular indefinite problems
 Singular leftdefinite problems
Part 5. Examples and other topics  Two intervals
 Examples
 Notation
 Comments on some topics not covered
 Open problems
 Bibliography
 Index
