Informace o publikaci
Half-linear dynamic equations
| Autoři | |
|---|---|
| Rok publikování | 2003 |
| Druh | Kapitola v knize |
| Fakulta / Pracoviště MU | |
| Citace | AGARWAL, Ravi P., Martin BOHNER a Pavel ŘEHÁK. Half-linear dynamic equations. In Nonlinear Analysis and Applications: To V. Lakshmikantham on his 80th Birthday, Ravi P. Agarwal, Donal O'Regan editors. Dordrecht: Kluwer Academic Publishers, 2003, s. 1-56. Volume 1. ISBN 1-4020-1688-3. |
| Popis | We survey half-linear dynamic equations on time scales. These contain the well-known half-linear differential and half-linear difference 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 definiteness 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. |
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