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.
2010
60 (5)
1421
1429
S. Matucci; P. Rehak;
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/774733
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