Integral averaging technique and oscillation of certain even order delay differential equations

Using the generalized Riccati technique and the averaging technique, new oscillation criteria for certain even order delay differential equation of the form

     

On oscillation of second order neutral type delay differential equations

Oscillation criteria are obtained by using the so called H-method for the second order neutral type delay differential equations of the form

(r(t)ψ(x(t))z^′(t))^′+q(t)f(x(σ(t)))=0, tt₀,

where z(t)=x(t)+p(t)x(τ(t)), r, p, q, τ, σ, C([t₀,∞),R) and f,ψC(R,R).

The results of the paper contains several results obtained previously as special cases. Furthermore, we are also able to fix an error in a recent paper related to the oscillation of second order nonneutral delay differential equations.     

New nonoscillation criteria for delay differential equations

This paper is concerned with the nonoscillation of first order delay differential equations of the form

     

Oscillation of first order delay differential equations with distributed delay

In this paper, we obtain some oscillation criteria for the first order delay differential equation with distributed delay

     

Asymptotic behavior of certain delay differential equations with forcing term

We study the asymptotic behavior of solutions of the following forced delay differential equation:

Some sufficient conditions that guarantee every solution of the equation to converge to zero are obtained. The results obtained are applied to some well-known delay differential ecological equations with forcing term.     

On nonexistence of Kneser solutions of third-order neutral delay differential equations

The aim of this paper is to complement existing oscillation results for third-order neutral delay differential equations by establishing sufficient conditions for nonexistence of so-called Kneser solutions. Combining newly obtained results with existing ones, we attain oscillation of all solutions of the studied equations.     

On the oscillation of solutions of first order differential equations with deviating arguments

1.IntroductionConsiderthefirstorderdifferentialequationwithdeviatingargUmelltTheoscillationofEq.(1)wasstudiedextensivelyinthelastthreedecades.See,forexamDleif--101andthereferencescitedtherein.In1972Ladas.LakshlnhanthamanddeceivedApril1,1997.Re~AugUBt...     

Oscillation properties of nonlinear impulsive delay differential equations and applications to population models

Comparison theorem and explicit sufficient conditions are obtained for oscillation and nonoscillation of solutions of nonlinear impulsive delay differential equations which can be utilized to population dynamic models. Our results in this paper generalize and improve several known results.     

On the logistic delay differential equations with piecewise constant argument and quasi-periodic time dependence

In this paper, we discuss the quasi-periodic logistic delay differential equations. As a corollary, we give a more sharp result than that in [G. Seifert, J. Differential Equations 164 (2000) 451-458] for the periodic logistic delay differential equations.     

Some oscillation results for second-order nonlinear delay dynamic equations

This paper is concerned with oscillatory behavior of a class of second-order delay dynamic equations on a time scale. Two new oscillation criteria are presented that improve some known results in the literature. The results obtained are sharp even for the second-order ordinary differential equations.     

Existence of positive solutions of nonlinear fractional delay differential equations

This paper investigates the existence and uniqueness of positive solutions for a class of nonlinear fractional delay differential equations. Using a nonlinear alternative of Leray-Schauder type, we show the existence of positive solutions for the equations in question.     

New oscillation criteria for second-order nonlinear neutral delay differential equations

In this paper, several new oscillation criteria for the second-order nonlinear neutral delay differential equation

     

时滞抛物方程解振动的充要条件

In this paper, necessary and sufficient conditions for oscillation of solu-tions of delay parabolic equations are obtained.     

Oscillation of first order delay differential equations with oscillating coefficients

In this paper,some sufficient conditions for oscillation of a first order delay differen-tial equation with oscillating coefficients of the form x^1(t) p(t)x(t-τ)=0 are established ,which improve and generalize some of the known results in the literature.     

Integral condition for oscillation of half-linear differential equations with damping

The purpose of this paper is to provide an oscillation theorem that can be applied to half-linear differential equations with time-varying coefficients. A parametric curve by the coefficients is focused in order to obtain our theorem. This parametric curve is a generalization of the curve given by the characteristic equation of the second-order linear differential equation with constant coefficients. The obtained theorem is proved by transforming the half-linear differential equation to a standard polar coordinates system and using phase plane analysis carefully.     

On the behavior of the solutions to periodic linear delay differential and difference equations

Some new results on the behavior of the solutions to periodic linear delay differential equations as well as to periodic linear delay difference equations are given. These results are obtained by the use of two distinct roots of the corresponding (so called) characteristic equation.     

Remarks on some families of fractional-order differential equations

The main purpose of this note is to draw the reader's attention towards some errors and omissions in a recent work involving solutions of some families of fractional-order differential equations, which was published in this Journal (see, for details, [Tomovski ?, Hilfer R, Srivastava HM. Fractional and operational calculus with generalized fractional derivative operators and Mittag–Leffler type functions. Integral Transforms Spec Funct. 2010;21:797–814]). Several relevant remarks and observations on some other related recent developments on this subject are also presented.