二阶非线性泛函微分方程解的振动性质

研究了一类二阶非线性泛函微分方程解的振动性以及非振动解的有界性.在一定条件下,建立了几个新的振动性和有界性定理,其结果推广和改进了已有的一些结果.     

高阶非线性阻尼脉冲微分方程解的振动性

研究了一类高阶非线性阻尼脉冲微分方程振动状态,得到振动解的充分条件.     

Oscillation criteria of a certain class of third order nonlinear delay differential equations with damping

In this paper, we are concerned with the oscillation of third order nonlinear delay differential equations of the form

(r₂(t)(r₁(t)y^′)′)′+p(t)y^′+q(t)f(y(g(t)))=0.     

一类偶数阶含阻尼项时滞微分方程解的振动性的判定

利用Riccati变换和辅助函数法,对一类偶数阶含阻尼项非线性时滞微分方程建立了判定其所有解振动的若干充分准则.     

Oscillation of nonlinear second order matrix differential equations

In this paper, sufficient conditions are obtained for oscillation of all nontrivial, prepared, symmetric solutions of a class of nonlinear second order matrix differential equations of the form

带有振动系数的一类高阶中立型非线性受迫微分方程的振动准则

在本文中,我们获得形如[y(t) l∑j=1pj(t)y(σj(t))](n) ∫0q(t,s)f(y(t s))dσ(s)=h(t)的带有振动系数的一类高阶中立型非线性受迫微分方程的振动准则.     

二阶非线性椭圆型微分方程解的振动比较定理

建立几个微分不等式,讨论了一类二阶非线性椭圆型微分方程解的振动性,得到几个新的振动比较定理．     

Oscillation criteria for odd‐order nonlinear delay differential equations with a middle term

The oscillation of solutions of the n th‐order delay differential equation was studied in [S. R. Grace and A. Zafer, Math. Meth. Appl. Sci. 2016, 39 1150–1158] when n is even and the n odd case has been referred to as an interesting open problem. In the present work, our primary aim is to address this situation. Our method of the proof that is quite different from the aforementioned study is essentially new. We introduce V _{n ?1}‐type solutions and use comparisons with first‐order oscillatory and second‐order nonoscillatory equations. Examples are given to illustrate the main results. Copyright © 2017 John Wiley & Sons, Ltd.     

Oscillation for systems of nonlinear neutral type parabolic partial functional differential equations

This paper discusses the oscillation of solutions for systems of nonlinear neutral type parabolic partial fuctional differential equations of the form     

Oscillation criteria for nonlinear second order differential equations with damping

Summary Using the integral average method, we give some new oscillation criteria for the second order differential equation with damped term (a(t)Ψ(x(t))K(x'(t)))'+p(t)K(x'(t))+q(t)f(x(t))=0, t<span style='font-size:10.0pt; font-family:"Lucida Sans Unicode"'>≧t₀. These results improve and generalize the oscillation criteria in<span lang=EN-US style='font-size:10.0pt;mso-ansi-language:EN-US'>[1], because they eliminate both the differentiability of p(t) and the sign of p(t), q(t). As a consequence, improvements of Sobol's type oscillation criteria are obtained.     

一类二阶非线性阻尼微分方程解的振动性质

研究了一类二阶非线性阻尼微分方程解的振动性质.在一定条件下,建立了四个新的振动性定理,推广和改进了已知的结果.     

Some new oscillation theorems for second order nonlinear elliptic equations with damping

In this paper, some new oscillation criteria are obtained for second order elliptic differential equations with damping of the form

     

Oscillation theorems for second order matrix differential systems

By employing the generalized Riccati technique and the integral averaging technique, new oscillation criteria are established for a class of second order matrix differential systems. These criteria extend, improve and unify a number of existing results and handle a number of cases not covered by known criteria. In particular, several interesting examples that illustrate the importance of our results are included. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

关于一类偶数阶半线性微分方程解的振动性的注记

通过运用分析方法,对微分不等式进行估计,得到了一类偶数阶半线性微分方程解的振动性的若干判别准则.所得结果减弱了已有文献的条件,推广和改进了已有文献的结果.     

Oscillation criteria and asymptotic properties of solutions of third‐order nonlinear neutral differential equations

The main goal of this article is to study the asymptotic properties and oscillation of the third‐order neutral differential equations with discrete and distributed delay. We give several theorems and related examples to illustrate the applicability of these theorems. Copyright © 2014 John Wiley & Sons, Ltd.     

Oscillation criteria for nth‐order nonlinear delay differential equations with a middle term

In this article, we establish some new criteria for the oscillation of nth‐order nonlinear delay differential equations of the form provided that the second‐order equation is either nonoscillatory or oscillatory. Examples are given to illustrate the results. Copyright © 2015 John Wiley & Sons, Ltd.     

New oscillation criteria for second order linear matrix differential equations with damping

By using the positive linear functional and the monotone subhomogeneous functional, including the general means and Riccati technique, some new oscillation criteria are established for the second order linear matrix differential system
（P（t）X＇（t））＇ ＋ R（t）X＇（t） ＋ Q（t）X（t） =0, t ≥ to 〉 0
where P（t）, R（t）, Q（t） are n × n real continuous matrix functions, P（t） and R（t） are commutative. Theresults improve and generalize those given in some previous papers, which can be seen by the examples given at the end of this paper.     

Oscillation of second‐order perturbed differential equations

We give constructive proof of the existence of vanishing at infinity oscillatory solutions for a second‐order perturbed nonlinear differential equation. In contrast to most results reported in the literature, we do not require oscillatory character of the associated unperturbed equation, monotonicity of nonlinearity, and we establish global existence of oscillatory solutions without assuming it a priori. Furthermore, as our example demonstrates, existence of bounded oscillatory solutions does not exclude existence of unbounded nonoscillatory solutions. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Some oscillation criteria for second order nonlinear functional ordinary differential equations

The main objective of this article is to study the oscillatory behavior of the solutions of the following nonlinear functional differential equations (a(t)x'(t))' δ1p(t)x'(t) δ2q(t)f(x(g(t))) = 0,for 0 ≤ t0 ≤ t, where δ1 = ±1 and δ2 = ±1. The functions p,q,g : [t0, ∞) → R, f :R → R are continuous, a(t) ＞ 0, p(t) ≥ 0,q(t) ≥ 0 for t ≥ t0, limt→∞ g(t) = ∞, and q is not identically zero on any subinterval of [t0, ∞). Moreover, the functions q(t),g(t), and a(t) are continuously differentiable.     

Oscillation theorems for second order quasilinear perturbed differential equations

Abstract. New oscillation criteria for the second order perturbed differential equation are pre-sented. The special case of the results includes the corresponding results in previous papers,extends and unifies a number of known results.