Half-linear Dynamic Equations: A Survey
We survey half-linear dynamic equations on time scales. These contain the well-known half-linear di erential and half-linear di erence equations as special cases, but also other kinds of half-linear equations. Special cases of half-linear equations are the well-studied linear equations of second order. We discuss existence and uniqueness of solutions of corresponding initial value problems and, using a Picone identity, derive a Reid roundabout theorem that gives conditions equivalent to disconjugacy of half-linear dynamic equations, among them solvability of an associated Riccati equation and positive de niteness of an associated functional. We also develop a corresponding Sturmian theory and discuss methods of oscillation theory, which we use to present oscillation as well as nonoscillation criteria for half-linear dynamic equations.
M. Bohner et al., "Half-linear Dynamic Equations: A Survey," Nonlinear Analysis and Applications, Kluwer Academic Publishers, Jan 2003.
Mathematics and Statistics
Keywords and Phrases
dynamic equations; time scales; half-linear equations; Sturmian theory; oscillation; Reid roundabout theorem; Picone Identity
Article - Journal
© 2003 Kluwer Academic Publishers, All rights reserved.
01 Jan 2003