Nonoscillation of half-linear dynamic equations

0346699 - MÚ 2011 RIV GB eng J - Journal Article
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. E-ISSN 1873-7668
R&D Projects: GA AV ČR KJB100190701
Grant - others:GA ČR(CZ) GA201/07/0145
Institutional research plan: CEZ:AV0Z10190503
Keywords : half-linear dynamic equation * time scale * (non)oscillation * Riccati technique
Subject RIV: BA - General Mathematics
Impact factor: 1.472, year: 2010
http://www.sciencedirect.com/science/article/pii/S0898122110004384

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.
Permanent Link: http://hdl.handle.net/11104/0187651