The half-linear dynamic equation on time scales is here considered. 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 wellstudied 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.
Nonoscillation of Half-Linear Dynamic Equations / S. Matucci; P. Rehak;. - In: COMPUTERS & MATHEMATICS WITH APPLICATIONS. - ISSN 0898-1221. - STAMPA. - 60 (5):(2010), pp. 1421-1429.
Nonoscillation of Half-Linear Dynamic Equations
MATUCCI, SERENA;
2010
Abstract
The half-linear dynamic equation on time scales is here considered. 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 wellstudied 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.File | Dimensione | Formato | |
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