[PDF] Top 20 3. Asymptotic behavior and oscillation of solutions of third order neutral dynamic equations with distributed deviating arguments

... (1.1) where T is a time scale unbounded above with t 0 ∈ T , z(t) = x(t) + p(t)x(g(t)), α i are quotients of positive odd integers for i = 1, 2, and a, b ∈ R with 0 < a < b. Standard notation and terminology for ... See full document

... to dynamic equations on time scales, or mea- sure chains, and we refer the reader to the landmark paper of Hilger [] for a comprehen- sive treatment of the ...the oscillation and ... See full document

... the oscillation theory and asymptotic behavior of various classes of second-order and high-order differential equations and dynamic equations on time scales ...the ... See full document

... the third-order neutral dynamic equations on time scales in the case p(t) ≥ ...the oscillation and asymptotic behavior of solutions of ... See full document

... Differential equations with delayed and advanced arguments (also called mixed differential equations or equations with mixed arguments) occur in many problems of economy, biology and ... 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

... first order delay equations and technique of Riccati transformation, we obtain a two different conditions ensure oscilla- tion of solutions of this equation, which extend and improve results of ...for ... See full document

... study asymptotic behavior and derive some new oscillation criteria for the cases without any restrictions on g(t) and σ (t) and when n is even and ... See full document

... differential equations have attracted noticeable interests due to their poten- tial applications in assorted fields, including physical sciences, technology, population dy- namics, and so ...of ... See full document

... In the special case when α = , (.) reduces to (.). Now the following question arises. Could we obtain new Philos-type oscillation criteria for (.) by using a generalized Riccati transformation which differs ... See full document

... The theory of time scales, which has recently received a lot of attention, was introduced by Hilger in his Ph. D. thesis [1] in order to unify continuous and discrete analysis. A time scale T is an arbitrary ... See full document

... In the aftermath of Hilger’s breakthrough paper [4], a rapidly diversifying body of literature has sought to unify, extend, and generalize ideas from discrete calculus, con- tinuous calculus, and quantum calculus to ... See full document

... differential equations with impulses, functional arguments and partial differential equations without im- pulses, functional arguments; from a practical standpoint, they are very convenient ... See full document

... 1) Equation (14) has a solution of type (D) if and only if σ < − − α 1 (Theorem 10 and 11). 2) Equation (14) has a solution of type (AC) if and only if σ < − − α 1 (Theorem 14). 3) Equation (14) has a ... See full document

... some oscillation criteria for solutions of ...general-type neutral dif- ferential ...the oscillation of solutions of ...positive solutions of some nonneutral di ff erential ... See full document

... In , Saker et al. [] posed an open problem as follows: How to establish oscillation criteria for equation (.) when condition (.) holds? Assuming (.), Zhang et al. [, ] obtained some sufficient ... See full document

... ential equations, especially for the first-order or second-order ...the oscillation for the second-order equations, researchers began to study the oscillation for the ... See full document

... In Section 2, we present some preliminary lemmas and in Section 3, we establish some sufficient conditions which ensure that all solutions of equation (1.1) are either oscillatory or con[r] ... See full document

... nonlinear neutral functional differential equations with distributed deviating ...the neutral coefficient, some new criteria are ... 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