二阶矩阵微分系统的区间振动准则

本文利用矩阵Riccati技巧,平均技巧及矩阵不等式,建立形如[P(t)Y']' Q(t)Y=0的二阶矩 阵微分系统的一些新的区间振动准则.所得结果推广,改进和包含一系列已有的结论,并能应用于已知 准则不能适用的若干情形.     

二阶矩阵微分系统的区间振动准则

本文利用矩阵Riccati技巧,平均技巧及矩阵不等式,建立形如[P(t)Y']'+Q(t)Y=0的二阶矩阵微分系统的一些新的区间振动准则.所得结果推广,改进和包含一系列已有的结论,并能应用于已知准则不能适用的若干情形.     

二阶线性矩阵微分系统的振动性

讨论了二阶线性矩阵微分系统(P(t)Y′(t))′+Q(t)Y(t)=0,t≥t0,其中P(t),Q(t) 和Y(t)是n×n实连续矩阵函数, P(t)和Q(t)是对称的且P(t)>0是正定矩阵．利用推广的Riccati变换,采用两种不同的方法,得到了该系统振动的若干判据．所得结果推广和改进了已知的相应结果．     

二阶线性矩阵微分系统的振动准则

本文利用广义Riccati变换,研究了一类二阶线性矩阵微分系统的振动性,得到了这类系统振动的若干新的判别准则.     

二阶线性矩阵微分系统的振动性

本文研究了矩阵微分系统（P（t）Y′）′＋Q（t）Y＝0,t∈［t0,∞）．其中P,Q和Y是n×n实连续矩阵函数,且P（t）和Q（t）是对称的．P（t）是正定矩阵（P（t）＞0,t∈［t0,∞））．利用推广的Riccati变换,得到了系统（1）振动的若干新判据．所得结果改进了Erbe,Kong和Ruan的相应结果．     

二阶非线性阻尼方程的振动准则

利用Riccati变换和积分平均方法,研究了一类具有阻尼项的二阶非线性方程的解为振动的若干充分条件,建立了一些判定上述方程为振动的充分准则,结果推广并加强了已有的一些振动准则．     

二阶非线性微分方程的振动性

本文利用Riccati技巧和平均技巧，研究一类二阶非线性微分方程的振动性，得到了这类方程振动的若干新的判别准则。     

二阶矩阵微分系统的振动性

通过Kummer变换,建立了线性矩阵微分系统(P(t)Y′)′ Q(t)Y=0的振动性判别准则,改进了文[4],[5]的振动性判别准则,并且简化了文[7]的证明．     

具有阻尼项的二阶自共轭矩阵微分系统的振动定理

运用Riccati技巧,正线性泛函和广义平均对方法,讨论具有阻尼项的二阶自共轭矩阵微分系统(P(t)Y’(t))’+r(t)P(t)Y’(t)+Q(t)Y(t)=0,t≥0,获得了一些新的振动定理.所得结果改进和推广了许多已知结论.特别地,补充了大量存在性结果,并能处理以前振动准则不能解决的问题.     

一类二阶非线性泛函微分方程的振动性

本文讨论二阶非线性泛函微分方程(a(t)y′(t))′+p(t)y′(t-τ(t))-q(t)f(y(t))=0,t≥t₀,(1)(a(t)y′(t))′-p(t)y′(t+τ(t))-q(t)f(y(t))=0,t≥t₀,(2)获得了方程(1)和(2)振动的充分性判据,推广和改进了已知的一些结果.     

Oscillation criteria related to integral averaging technique for linear matrix Hamiltonian systems

By employing a generalized Riccati technique and an integral averaging technique, new oscillation criteria are established for the linear matrix Hamiltonian system U′=A(x)U+B(x)V, V′=C(x)U−A∗(x)V under the assumption that all A(x), B(x)=B∗(x)>0, and C(x)=C∗(x) are n×n matrices of real-valued continuous functions on the interval I=[x₀,∞) (−∞<x₀). These criteria extend, improve, and unify a number of existing results and also handle cases not covered by known criteria. Several interesting examples that illustrate the importance of our results are included.     

具有散度形式的拟线性椭圆型微分方程的区域振动准则

对一类具有散度形式的拟线性椭圆型微分方程建立了若干新的振动准则,所得结果仅依赖于方程在外区域Ω(?)R~n的一个区域序列的信息而有别于已知的大多数结论.     

Oscillation criteria for third-order nonlinear differential equations

In this paper, we are concerned with the oscillation properties of the third order differential equation

Oscillation of second-order nonlinear neutral dynamic equations on time scales

This paper is concerned with the oscillation of second-order nonlinear neutral dynamic equations of the form

(r(t)((y(t)+p(t)y(τ(t)))^Δ)^γ)^Δ+f(t,y(δ(t)))=0,     

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.     

Interval criteria for oscillation of second-order half-linear differential equations

By employing a generalized Riccati technique and an integral averaging method, interval oscillation criteria are established for the second-order half-linear differential equation [r(t)|x′(t)|^α−1x′(t)]′+q(t)|x(t)|^α−1x(t)=0. These criteria are different from most known ones in the sense that they are based on information only on a sequence of subintervals of [t₀,∞), rather than on the whole half-line. They also extend, improve, and complement a number of existing results, and can be applied to extreme cases such as . In particular, several interesting examples that illustrate the importance of our results are included.     

OSCILLATION CRITERIA FOR NONLINEAR SECOND ORDER ELLIPTIC DIFFERENTIAL EQUATIONS

1.IntroductionOscillationtheoryforellipticdifferentialequationswithvariablecoefficielltshasbeenextensivelydevelopedinrecentyearsbymanyauthors(seee-g-,Allegretto[1,2l,Bugir['],Fiedler[5]'KitamuraandKusano['],Kural4]KusanoandNaitol1o]'NaitoandYoshidal12]'NoussairandSwanson[l3'14]'Swansonl15'l6]andthereferencescitedtherein).Inthispaper,weareconcernedwiththeoscillatorybehaviorofsolutionsofsecondorderellipticdifferelltialequatiollswithalternqtingcoefficients.Asusual,pointsinn-dimensionalEucli…     

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.     

二阶非线性矩阵微分方程的振动性

Some new oscillation criteria are established for the second-order matrix differential system(r(t)Z′(t))′ p(t)Z′(t) Q(t)F(Z′(t))G(Z(t)) = 0, t ≥ to ＞ 0,are different from most known ones in the sense that they are based on the information only on a sequence of subintervals of [t0, ∞), rather than on the whole half-line. The results weaken the condition of Q(t) and generalize some well-known results of Wong (1999) to nonlinear matrix differential equation.