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.
- dynamic equations,
- time scales,
- half-linear equations,
- Sturmian theory,
- oscillation,
- Reid roundabout theorem,
- Picone Identity
Available at: http://works.bepress.com/martin-bohner/46/