[PDF] Top 20 Existence of Nonoscillatory Solutions to Second Order Neutral Delay Dynamic Equations on Time Scales

... 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 ...of time scales, by ... See full document

... A time scale T is an arbitrary nonempty closed subset of the real ...of time scales. On a time scale T , the forward jump operator, the backward jump operator and the graininess function are ... See full document

... of solutions of various equations on time scales, and we refer the reader to ...the existence of positive solutions of the delay ... See full document

... the existence of nonoscillatory solutions of equation ...the existence of the nonoscillatory solu- tions tending to zero as t → ∞ of equation () were exceptional, and as a result, the ... See full document

... Tuncay Candan received his M.Sc and Ph.D degree in Applied Mathematics from the Department of Mathematics at Iowa State University, USA. He is currently a Professor of Mathematics at American University of the Middle ... See full document

... of time scales in his ...of time scale calculus can be found in [–] and omitted ...the existence of nonoscilla- tory solutions to neutral dynamic equations on ... See full document

... Remark 3.4 It is not easy to find a sufficient condition for the existence of nonoscillatory solutions tending to zero to (1) since their asymptotic behaviors are more complex than those of other ... 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

... x(t) + p(t)x(t − τ ) + q(t)G x(t − σ) = f (t) (2) Also, sufficient conditions are obtained for existence of bounded nonoscillatory solutions of (2). The motivation of the present work come from the ... See full document

... Selvam, Existence of Nonoscillatory Solutions of Second Order Linear Neutral Delay Difference Equations with Forcing term, International Journal of Engineering ... See full document

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

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

... for second order nonlinear neutral delay dynamic equations on time scales, ...quasi-linear neutral delay dynamic equations 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, which unifies continuous and discrete analysis, was first introduced by Hilger ...for dynamic equations on time scales has recently received a lot of attention, ... 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

... However, to the best of our knowledge, there does not appear to be any results for the third-order neutral dynamic equations on time scales in the case p(t) ≥ . The main aim of ... 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

... Obviously, under the case (1.3), Theorem 1.2 (the other results are the same, for example, Theorem 4.3 and Theorem 4.4 in [2], Theorem 3.5 in [9], etc.) cannot ensure that the solution x(t) of Eq. (1.1) is oscillatory. ... 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