Oscillation Theory of Two-Term Differential Equations
Publisher: Springer Netherlands
Published: December 28, 2009
Format: Paperback
Number of pages: 236
ISBN-13: 9789048148066
First sentence: In this chapter we summarize some basic concepts of oscillation theory of n-th order linear ordinary differential equations.
Description: This volume is about oscillation theory. In particular, it considers the two-term linear differential equations Lny + p(x)y = 0, where Ln is a disconjugate operator of order n and p(x) has a fixed sign. Special attention is paid to the equation y(n) + p(x)y = 0. These equations enjoy a very rich structure and are the natural generalization of the Sturm-Liouville operator. Our aim is to introduce an order among the results which are distributed over hundreds of research papers, and arrange them in a unified and self-contained way. Many new proofs are given and the original proof is never copied verbatim. Numerous new results are included. Among the topics which are discussed are oscillation and nonoscillation, disconjugacy, various types of disfocality, extremal configurations of zeros, comparison theorems, classification of solutions according to their behaviour near infinity and their dominance properties. Audience: This work will be of interest to researchers and graduate students interested in the qualitative theory of differential equations.