[PDF] Top 20 22. Oscillation theorems for fourth-order delay dynamic equations on time scales

... 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

... of dynamic equations on time scales, which goes back to Hilger [], provides a rapidly expanding body of literature where the main idea is to unify, extend, and generalise concepts from ... 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

... 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

... A time scale T is an arbitrary nonempty closed subset of the real ...of time scales was introduced by Hilger [6] in his ...in order to unify continuous and discrete ... See full document

... of time scales, which has recently received a lot of attention, was introduced by Hilger in his ...in order to unify continuous and discrete analysis see Hilger 1 ...of time scales, by ... 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

... 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

... of oscillation and stability of delay dynamic equations on time ...on oscillation and existence of nonoscillatory solutions for dynamic equations can be found in ... See full document

... quotient of odd positive integers with r , a, and p real-valued positive rd-continuous functions defined on T. To the best of our knowledge nothing is known regarding the qualitative behavior of these equations on ... See full document

... in delay ξ( t ) ≤ t and non-delay ξ( t ) = t cases, where n ≥ 2 is a positive integer, l is the ratio of positive odd ...higher order difference equations and differential equations are ... 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

... consider oscillation criteria for certain third-order delay and advanced dynamic equations on unbounded time ...A time scale T is a nonempty closed subset of the real ... See full document

... with oscillation and asymptotic behavior of a second-order neutral delay dynamic equation on an arbitrary time ...two theorems which guarantee that every solution of the studied ... See full document

... the oscillation and nonoscillation of solutions of various equations on time scales; we refer the reader to the papers [–] and the references cited ...the oscillation results for ... 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

... 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

... on time scales  , where α ≥ 1 is a quotient of odd positive integers. Ap- plying the inequality technique we present two new sufficient conditions which ensure that every solution of equations is ... See full document

... new oscillation criteria for the second-order nonlinear delay dynamic equations r tx Δ t γ Δ ptfxτ t 0 on a time scale T; here γ > 0 is a quotient of odd positive integers ... See full document

... a time scale T, where γ ≥  is the quotient of odd positive integers, a and r are positive rd-continuous functions on T, and the so-called delay function τ : T → T satisfies τ (t) ≤ t for t ∈ T and lim t→∞ τ ... See full document