Nonlinear Analysis and Application: To V. Lakshmikantham in his 80th Birthday

0021730 - MÚ 2006 RIV NL eng M - Část monografie knihy
Agarwal, R. P. - Bohner, Martin - Řehák, Pavel
Half-linear dynamic equations.
[Pololineární dynamické rovnice.]
Nonlinear Analysis and Application: To V. Lakshmikantham in his 80th Birthday. Dordrecht: Kluwer Academic Publishers, 2003 - (Agarwal, R.; O´Regan, D.), s. 1-56
Grant ostatní: GA ČR(CZ) GA201/01/0079; GA ČR(CZ) GP201/01/P041
Výzkumný záměr: CEZ:AV0Z1019905
Klíčová slova: dynamic equations * time scales * half-linear equations
Kód oboru RIV: BA - Obecná matematika

We survey half-linear dynamic equations on time scales. These contain the well-know 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 hall-linear dynamic equations.

Článek prezentuje přehled výsledku v teorii pololineárních dynamických rovnic, které sjednocují diferenciální a diferenční rovnice a rovněž jiné typy pololineárních rovnic. Zejména je diskutována otázka existence a jednoznačnosti počátečního problému a oscilační teorie.
Trvalý link: http://hdl.handle.net/11104/0110630