Oscillation criteria for a class of second-order neutral delay differential equations

In this article, we investigate oscillation and asymptotic behaviour of all solutions of a class of neutral delay differential equations of second-order with several positive and negative coefficients having the form

where R,P,Q are bounded beginning segments of positive integers, , , are delay functions and f is a continuous function. Our results improve and extend the recent results given in the papers [J. Manojlović, Y. Shoukaku, T. Tanigawa, N. Yoshida, Oscillation criteria for second-order differential equations with positive and negative coefficients, Appl. Math. Comput. 181 (2006) 853–863] and [A. Weng, J. Sun, Oscillation of second order delay differential equations, Appl. Math. Comput. 198 (2) (2008) 930–935].     

Asymptotic behavior of solutions of neutral differential equations with positive and negative coefficients

Sufficient conditions are established for the asymptotic behavior of solutions of neutral differential equations with positive and negative coefficients

     

Oscillation criteria for first-order neutral nonlinear difference equations with variable coefficients

Consider the first-order neutral nonlinear difference equation of the form

, where τ > 0, σ_i ≥ 0 (i = 1, 2,…, m) are integers, {p_n} and {q_n} are nonnegative sequences. We obtain new criteria for the oscillation of the above equation without the restrictions Σ_n=0^∞ q_n = ∞ or Σ_n=0^∞ nq_n Σ_j=n^∞ q_j = ∞ commonly used in the literature.     

Oscillation of neutral differential equation with positive and negative coefficients

In this paper, we provide oscillation properties of every solution of the neutral differential equation with positive and negative coefficients

[x(t)−R(t)x(t−r)^]′+P(t)x(t−τ)−Q(t)x(t−σ)=0,     

Oscillation criteria for first-order neutral differential equations

This paper discusses a class of first-order neutral differential equations with variable coefficients and variable deviations. A series of sufficient conditions are established for all solutions of the equations to be oscillatory, and some of the conditions are sharp.     

Oscillation criteria for second-order linear differential equations

In this paper, we obtain some oscillation criteria for the second-order linear differential equation x″(t)+p(t)x(t)=0.     

正负系数中立型差分方程的正解的存在性

In this paper the sufficient conditions for the existence of positive solutions of the neutral difference equations with positive and negative coefficients are established. The results improve some known conclusions in the literature     

正负系数中立型差分方程的全局吸引性

A neutral difference equation with positive and negative coefficients△(xn-cnxn-k) pnxn-l-qnxn-r=0,n=0,1,2.…，is considered and a sufficient condition for the global attractivity of the zero solution of this equation is obtained, which improves and extends the all known results in the literature.     

Oscillation and nonoscillation criteria for quasilinear differential equations

Some oscillation and nonoscillation criteria for quasilinear differential equations of second order are obtained. These results are extensions of earlier results of Huang (J. Math. Anal. Appl. 210 (1997) 712-723) and Elbert (J. Math. Anal. Appl. 226 (1998) 207-219).     

Comparison criteria of positive solutions for a neutral difference equation with positive and negative coefficients

1.IntroductionInthispaper,weareconcernedwithaclassofneutraltypeflorenceequationswithpositiveandnegativecoefficielltsoftheformwhere',TandaarepositiveintegerssuchthatT2a){r'}:,isarealsequence3{p'}:,and{qn}Zoarenonnegativesequences.Similarequationshaver...     

具有正负系数的中立型微分方程的振动性

研究具有正负系数的中立型微分方程（x(t)-Cx(t-r)‘ px(t-τ)-qx(t-σ)=0,在允许C q(τ-σ)≤1不成立的条件下,建立了方程（*）的振动性准则。     

Oscillation criteria for second-order nonlinear differential equations with integrable coefficient

In this paper, we consider the second-order nonlinear differential equation

[a(t)|y′(t)|^σ−1y′(t)|′+q(t)f(y(t))=r(t)

where σ > 0 is a constant, a C(R, (0, ∞)), q C(R, R), f C(R, R), xf(x) > 0, f′(x) ≥ 0 for x ≠ 0. Some new sufficient conditions for the oscillation of all solutions of (*) are obtained. Several examples which dwell upon the importance of our results are also included.     

Periodic boundary value problem for first-order impulsive ordinary differential equations

This paper investigates the existence of minimal and maximal solutions of the periodic boundary value problem for first-order impulsive differential equations by establishing two comparison results and using the method of upper and lower solutions and the monotone iterative technique.     

Almost periodic solutions for forced perturbed impulsive differential equations

Sufficirnt condition for the existence of almost periodic solutions of forced perturbed systems of impulsive differential equations with impulsive effect at fixed Moments are considered.     

Oscillation criteria for delay equations

This paper is concerned with the oscillatory behavior of first-order delay differential equations of the form

(1)

where is non-decreasing, for and . Let the numbers and be defined by

It is proved here that when and all solutions of Eq. (1) oscillate in several cases in which the condition

2k+\frac{2}{{\lambda}_{1}}-1 \end{displaymath}">

holds, where is the smaller root of the equation .

     

Oscillation of fourth order sub-linear differential equations

In this paper, we deal with oscillatory and asymptotic properties of solutions of a fourth order sub-linear differential equation with the oscillatory operator. We establish conditions for the nonexistence of positive and bounded solutions and an oscillation criterion.     

Existence of nonoscillatory solutions for system of fractional differential equations with positive and negative coefficients

In this paper we consider the system of fractional differential equations with positive and negative coefficients. We use the $Banach$ contraction principle to obtain new sufficient conditions for the existence of nonoscillatory solutions.     

Neutral delay differential equations with positive and negative coefficients

Consider the neutral delay differential equation [display math001] where [display math002] We studied the asymptotic behavior of the nonoscillatory solutions of Eq. (1) and we obtained sufficient conditions for the oscillation of all solutions, all bounded solutions, and all unbounded solutions of Eq. (1)     

Oscillation criteria for second order forced ordinary differential equations with mixed nonlinearities

We present new oscillation criteria for the second order forced ordinary differential equation with mixed nonlinearities:

     

Oscillation of impulsive partial difference equations with continuous variables

This paper is devoted to a class of linear impulsive partial difference equations with continuous variables. We establish a difference inequality without impulses, and use it to obtain various sufficient conditions for the oscillation of solutions.