Half-linear dynamic equations

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F03%3A00021730" target="_blank" >RIV/67985840:_____/03:00021730 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Half-linear dynamic equations
Original language description
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 arethe 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 ofhalf-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.
Czech name
Pololineární dynamické rovnice
Czech description
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.

Publication year
2003
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Book/collection name
Nonlinear Analysis and Application: To V. Lakshmikantham in his 80th Birthday
ISBN
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Number of pages of the result
56
Pages from-to
1-56
Number of pages of the book
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Publisher name
Kluwer Academic Publishers
Place of publication
Dordrecht
UT code for WoS chapter
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