[PDF] Top 20 Nonoscillatory solutions for first order neutral dynamic equations with continuously distributed delay on time scales

... of nonoscillatory solutions to the first-order neutral dynamic equa- tion ...of nonoscillatory solutions for other dynamic ... See full document

... on a time scale T, where γ is the quotient of odd positive integers. By using a generalized Riccati transformation and an integral averaging technique, we establish some new sufficient conditions which ensure that ... See full document

... In the proof of Theorem 2.3, first (2.1) is reduced to a first-order delay dynamic equation in the form of (2.2) and then, by similar steps of the proof of well-known oscillation ... 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

... of solutions of various equations on time-scales; we refer the reader to the papers 6–38 ...third-order dynamic equations; see, for example, 14– 16, 21, 35 ... 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

... of time scale was initiated by Hilger’s landmark paper [] in order to cre- ate a theory that can unify discrete and continuous analysis, which has received a lot of ...interesting time ... See full document

... difference equations have been developed rapidly in the recent ...of time scale united the differential and difference ones, and since then many researchers have investi- gated the oscillation and ... See full document

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

... Recall that in this paper we consider only the case where the coe ffi cient function p in (1.1) is nonconstant but bounded. Before stating the main results, we need the following lemma, which is a version of the ... See full document

... bounded nonoscillatory solutions for equation ...bounded nonoscillatory solutions and discuss the errors estimates between the iterative approximations and the bounded nonoscillatory ... See full document

... so that y n (t) is eventually of one-signed. Hence, lower-order derivatives y i (t) , 0 ≤ i ≤ n - 1, are monotone and one-signed eventually. We must have y(t) >0, since other- wise we obtain a contradiction ... See full document

... establish several new oscillation criteria for the equation by employing Kiguradze’s lemma, the Taylor monomials on time scales and a generalized Riccati technique. The obtained results extend and ... See full document

... Zhang and Wang Advances in Difference Equations (2015) 2015 7 DOI 10 1186/s13662 014 0337 y R E S E A R C H Open Access Oscillation of second order nonlinear neutral dynamic equations with distributed[.] ... See full document

... above equations, the delay of neutral part in the discussed differential equations were all constant ...for distributed deviating arguments is rather rare; see [, ...higher-order ... 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 ...of time scale, by Bohner and ... See full document

... positive solutions to a class of nonlinear first-order periodic boundary value problems of impulsive dynamic equations on time scales are ... 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