[PDF] Top 20 Oscillation and nonoscillation for second order neutral dynamic equations with positive and negative coefficients on time scales

... the oscillation and nonoscillation of solutions of dynamic equations on time scales since Hilger introduced the theory of time scale which was excepted to unify continuous ... See full document

... Proof On the contrary, let y(t) be a nonoscillatory solution of Eq. (1). Without loss of generality, it can be assumed that y(t) is an eventually positive solution. Moreover, let u(t) be the same as defined in (2) ... See full document

... the oscillation of ...on time scales up to ...the oscillation of (). We obtain some oscillation criteria for () by developing a generalized Riccati substitution ... 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 ... See full document

... negative. If z(t) is eventually positive, the lemma is proved. If z(t) is eventually negative, we see that lim t→∞ z(t) exists. Assume that lim t→∞ z(t) < . Similarly as in the proof of Lemma ... See full document

... Philos-type oscillation criteria for second order nonlinear neutral delay dynamic equations on time scales, ...Long, Oscillation criteria for quasi-linear ... 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 ... See full document

... difference equations has received much attention in recent years due to its extensive applications in computer, probability theory, queuing problems, sta- tistical problems, stochastic time series, ... See full document

... a time scale ...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, ξ ) : T × [a, b] → T is rd-continuous function such that ... See full document

... of (1.1) is called oscillatory if it is neither eventually positive nor eventually negative; otherwise it is called nonoscillatory. Equation (1.1) is called oscillatory if all solutions are oscillatory. Our ... See full document

... concerning oscillation and nonoscillation of solutions to neutral differential and dynamic equations on time scales, we refer the reader to [, ] and [–], and the ... See full document

... According to the solution of (1), we mean a nontrivial real-valued function x satisfying (1) for t ∈  . We re- call that a solution x of Equation (1) is said to be oscillatory on [ t 0 , ∞ )  in case it is neither ... See full document

... 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

... delay dynamic equation which has been consid- ered by some authors and some oscillation and nonoscillation results have been obtained [, , ...the second-order delay dynamic ... See full document

... 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

... new oscillation criteria under very mild conditions and more general assumptions to extend the above results for the neutral delay and mixed dynamic ... See full document

... advanced dynamic equation on time scales, such as the h- difference equation (h > 0), and it is also called a finite difference equation, ...differential equations on time ... 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

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

... the oscillation of solution of second-order damped dynamic equations on time scale which attempts to harmonize the oscillation theory for continuousness and discreteness, ... See full document