Hille-Kneser-type criteria for second-order dynamic equations on time scales | Zendy

Lynn Erbe | Zendy; Allan Peterson | Zendy; Samir H. Saker | Zendy

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Hille-Kneser-type criteria for second-order dynamic equations on time scales

Author(s) -

Lynn Erbe,

Allan Peterson,

Samir H. Saker

Publication year - 2006

Publication title -

advances in difference equations

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.67

H-Index - 51

eISSN - 1687-1847

pISSN - 1687-1839

DOI - 10.1155/ade/2006/51401

Subject(s) - mathematics , ordinary differential equation , type (biology) , partial differential equation , order (exchange) , dynamic equation , mathematical analysis , differential equation , nonlinear system , geology , physics , economics , paleontology , finance , quantum mechanics

We consider the pair of second-order dynamic equations, (r(t)(xΔ)γ)Δ + p(t)xγ(t) = 0 and (r(t)(xΔ)γ)Δ + p(t)xγσ(t) = 0, on a time scale T ,w here γ> 0 is a quotient of odd positive integers. We establish some necessary and sufficient conditions for nonoscilla- tion of Hille-Kneser type. Our results in the special case when T = R involve the well- knownHille-Kneser-typecriteriaofsecond-orderlineardifferentialequationsestablished by Hille. For the case of the second-order half-linear differential equation, our results ex- tend and improve some earlier results of Li and Yeh and are related to some work of Dosl´ y and ˇ Reh´ ak and some results of ˇ

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