In the paper, the existence of positive solutions is studied for the second-order delay differential equation with a damping term ẍ(t)+ a(t)ẋ(t)+ b(t)x(h(t)) = 0 using a comparison with the integro-differential equation ẏ(t)+ ∫ t t0 e ∫ t s a(ξ)dξb(s)y(h(s))ds = 0. Explicit non-oscillation criteria and comparison type results are derived. © 2010 Elsevier Ltd. All rights reserved.

In this paper, the existence of mild solutions for the fractional differential equations of neutral type with infinite delay is obtained under the conditions in respect of the Kuratowski’s measure of noncompactness. As an application, the existence of mild solution for some integrodifferential equation is obtained. keywords: fractional differential equation, neutral differential equation, mild ...

Article history: Received 20 November 2015 Received in revised form 8 March 2016 Accepted 25 March 2016 Available online 31 March 2016

in this article differential transformation method (dtms) has been used to solve neutral functional-differential equations with proportional delays. the method can simply be applied to many linear and nonlinear problems and is capable of reducing the size of computational work while still providing the series solution with fast convergence rate. exact solutions can also be obtained from the kno...

In this paper we studyC0-semigroups onX×Lp(−h, 0;X) associated with linear differential equations with delay, whereX is a Banach space. In the case thatX is a Banach lattice with order continuous norm, we describe the associated modulus semigroup, under minimal assumptions on the delay operator. Moreover, we present a new class of delay operators for which the delay equation is well-posed for p...

Asymptotic properties and estimate of singular solutions (either defined on a finite interval only or trivial in a neighbourhood of ∞) of the second order delay differential equation with p-Laplacian are investigated.