[PDF] Top 20 On the Oscillation of Second Order Nonlinear Neutral Delay Dynamic Equations on Time Scales

... On the Oscillation of Second-Order Nonlinear Neutral Delay Dynamic Equations on Time Scales Quanxin Zhang, Xia Song, Li Gao Department of Mathematics, Binzhou University, Shandong, China[r] ... See full document

... various equations on time scales, we refer the reader to the papers which deal with the first-order dynamic equations [5–7] and second-order dynamic ... See full document

... A time scale T is an arbitrary nonempty closed subset of the reals R ...of dynamic equations on time scales is a fairly new topic, and work in this area is rapidly ...a dynamic ... See full document

... the oscillation and nonoscillation of solutions of various equations on time scales, and we refer the reader to Bohner and Saker [5], Erbe [6], Erbe et ...the oscillation of the ... See full document

... the oscillation theory of dynamic equations on time scales has become one of the research ...of second-order nonlinear delay dynamic equation ... See full document

... the oscillation and non-oscillation of solutions of dynamic equations on time ...with second-order dynamic equations whereas for higher order ... See full document

... of dynamic equations on time scales, we refer the reader to [1–23] and the references cited ...particular, oscillation of dynamic equations with damp- ing attracted ... See full document

... where p and q are positive, real-valued rd-continuous functions defined on T, τ : T → T is rd-continuous, τ t ≤ t and τ t → ∞ as t → ∞, and f ∈ CR, R satisfies for some positive constant L, |fx| ≥ L|x|, xf x > 0 for ... See full document

... some oscillation criteria for ...half-linear delay dynamic equation (.) on time scales, where  < α ≤  is the quotient of odd positive integers and established some suf- ficient ... See full document

... The paper is organized as follows. In the next section, by developing a Riccati transformation technique some sufficient conditions for oscillation of all solutions of 1.1 on time scales are ... See full document

... S.enel, Oscillation theorems for the second order damped nonlinear dynamic equation on time scales, Contemp. Zhang, Oscillation of second-order half-linear delay dynamic equations with d[r] ... See full document

... the oscillation and nonoscillation of solutions of various equations on time scales, and we refer the reader to Bohner and Saker 5 , Erbe 6 , and Hassan 7 ...the oscillation of the ... See full document

... the oscillation and nonoscillation of solutions of various equations on time-scales; we refer the reader to the papers 6–38 ...few oscillation results for the oscillation of ... See full document

... The purpose of this note is to derive some new oscillation criteria for Eq. (1.1). The organization of this paper is as follows: In the next section, we present the basic definitions and the theory of calculus on ... See full document

... Dynamic equations with deviating argument are deemed to be adequate in modeling of the countless processes in all areas of ...of delay dynamic equations under consideration is the ... See full document

... of time scales was introduced by Hilger [1] in order to unify, extend and generalize ideas from discrete calculus, quantum calculus and continuous calculus to arbitrary time scale ...of ... See full document

... on a time scale T. Throughout this paper, it is assumed that γ ≥  is a quotient of odd positive integers,  < a < b, τ (t) : T → T, is rd-continuous function such that τ (t) ≤ t and τ (t) → ∞ as t → ∞, δ(t, ... See full document

... of τ(t) ≤ t, assumption τ(δ(t)) < t is already satisfied when δ(t) < t and the proofs do not change. Assumption τ(t) < t implies the immediate result τ(δ(t)) < δ(t). Therefore, we conclude the following which ... See full document

... Saker, Asymptotic Behavior of Solutions of a Third-Order Non-linear Dynamic Equation on Time Scales, Journal of Computational and Applied Mathematics 181, (2005) 92-102. Thandapani, O[r] ... See full document

... In , Candan [] discussed the oscillation of Eq. (.) for δ(t, ξ ) ≤ t and δ(t, ξ) > t, respectively, where γ >  is a quotient of odd positive integers. In [], δ(t, ξ ) is decreasing with respect to ξ ... See full document