Počet záznamů: 1

Nonoscillation of half-linear dynamic equations

  1. 1.
    0346699 - MU-W 2011 RIV GB eng J - Článek v odborném periodiku
    Matucci, S. - Řehák, Pavel
    Nonoscillation of half-linear dynamic equations.
    Computers & Mathematics With Applications. Roč. 60, č. 5 (2010), s. 1421-1429 ISSN 0898-1221
    Grant CEP: GA AV ČR KJB100190701
    Grant ostatní: GA ČR(CZ) GA201/07/0145
    Výzkumný záměr: CEZ:AV0Z10190503
    Klíčová slova: half-linear dynamic equation * time scale * (non)oscillation * Riccati technique
    Kód oboru RIV: BA - Obecná matematika
    Impakt faktor: 1.472, rok: 2010

    The half-linear dynamic equation on time scales is here considered, under the condition . Two new characterizations of nonoscillation to this equation are provided, namely in terms of solvability to a related weighted integral Riccati type inequality and in terms of the convergence of a certain function sequence involving the coefficients r and p. These relations are then applied to obtain new oscillation criteria and a comparison theorem, which extend the results known from the continuous or the linear case. The results are new even in the well-studied difference equation setting. A basic classification of nonoscillatory solutions to the equation is also presented. The paper is concluded by indicating some directions for a future research.
    Trvalý link: http://hdl.handle.net/11104/0187651
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