[PDF] Top 20 On Periodic Solutions of Higher-Order Functional Differential Equations

... a periodic solution of nonautonomous differential equations,” Differentsial’nye Uravneniya, ...Differential Equations, ...“On periodic solutions of even-order ordinary differential ... See full document

... almost periodic on R if, for any ε > 0, there exists a real number l = l(ε) > 0 with the property that, for any interval with length l(ε), it is possible to find a number δ = δ(ε) in this interval such that | ... See full document

... semicontinuous functional whose Gâteaux derivative admits a continuous inverse on X ∗ , and is a continuously Gâteaux differentiable func- tional whose Gâteaux is ... See full document

... Proof From Lemma ., we have obtained that Eq. (.) has at most one T -periodic so- lution. Thus, to prove Theorem ., it suffices to show that Eq. (.) has at least one T -periodic solution. To do this, ... See full document

... In this paper, by utilizing the fixed point index in cones, we prove the existence of positive periodic solutions for the general third-order Eq. (1.1). The results are obtained in the case that f ... See full document

... Mao and Liu Advances in Difference Equations 2014, 2014 33 http //www advancesindifferenceequations com/content/2014/1/33 R ES EARCH Open Access On the growth of solutions of certain higher order line[.] ... See full document

... Lemma 2.9 [10] Let 𝑓(𝑧)"“be an entire function of order“ 𝜌 “where“ "0" < 𝜌 < "1/2 ,“and let“ 𝜀 > 0 “be a given constant.“Then there exists a set“𝐸 ⊂ ["0, ∞)" with“𝑑𝑒𝑛𝑠 ̅̅̅̅̅̅̅𝐸 ≥ ... See full document

... Differential equations involving impul- sive effects occur in many applications: physics, population dynamics, ecology, biological systems, biotechnology, industrial robotic, pharmacokinetics, optimal control, ... See full document

... differential equations has been a significant development in the last two ...decades. Periodic solutions and periodic boundary value problems of impulsive differential equations have ... See full document

... Theorem . extends and unifies two results recently obtained by the authors in [] and []. In [] the ambient manifold M is not necessarily compact, but our investigation regards delay differential equations with ... See full document

... = r(t)x ′ (t − τ (t)) + f (t, x(t), x(t − τ(t))). By using Krasnoselskii’s fixed point theorem and the con- traction mapping principle, established some criteria for the existence and uniqueness of periodic ... See full document

... Here we are concerned with the existence and the asymptotic properties of the positive continuable solutions of the functional differential equation.. and ft,y is positive, continuous, a[r] ... See full document

... Delay differential equations have received increasing attention during recent years since these equa- tions have been proved to be valuable tools in the modeling of many phenomena in various fields of ... See full document

... positive periodic solutions to second order differential equations with singular nonlinear ...positive solutions under reasonable ... See full document

... differential equations; see 1 and the references ...of functional differential equations ...of periodic boundary value problems for second-order differential equation; the condition α0 αT ... See full document

... Theorem . and the remaining theorems involve the logarithmic measure and densities of set, which will be recalled in Section . In this paper, we study the growth of solutions of (.) and (.), and one of the ... See full document

... neutral functional differential equations, while studies on higher-order neutral functional differential equations are rather infrequent, especially on higher-order ... See full document

... By the integral mean value theorem, there exists a constant ξ ∈ (, T ) such that g( –r  x(ξ + s)dα(s)) – q = . So (H) implies that | –r  x(ξ + s) dα(s) | ≤ M. Since  –r (α) =  and α(–r) = α() on t ∈ [–r, ], by ... See full document

... non-linear functional differential equations (see Remark ...the periodic boundary value ...the solutions of ()-() for non-negative f ... See full document

... Proof of Theorem 1.2 Since g Î C 1 [m, M], max{g’(u): m ≤ u ≤ M} exists and max {g ’ (u): m ≤ u ≤ M} ≥ 1. Let p = max{g ’ (u): m ≤ u ≤ M}. If p = 1, then g(u) ≡ u on [m, M]. It is easy to check that any constant c Î [m, ... See full document