高阶变系数函数方程的非振动解

给出一类高阶非线性函数方程的一些新的非振动准则,并且给出了在差分方程中的若干应用,结果改进和推广了近期文献的某些结果.     

Oscillatory and asymptotic behaviour of a nonlinear second order neutral differential equation

In this paper, necessary and sufficient conditions for the oscillation and asymptotic behaviour of solutions of the second order neutral delay differential equation (NDDE)

OSCILLATION AND NON-OSCILLATION FOR SECOND-ORDER QUASI-LINEAR DIFFERENCE EQUATIONS

Some oscillation and non-oscillation criteria for second-order quasi-linear difference equations are given. The results in Zhang and Zhou [4] are improved.     

一般Volterra-Stieltjes微积分方程的比较定理

In this paper, A. B, Mingarelli‘s result is generalized to General Volterra-Stieltjes Integro-differential Equations. Comparison theorem and equivalence condition of non-oscillation are obtained.Clasical Sturm comparison theorem and some conclusions are generalized.     

Oscillation of fourth order nonlinear neutral difference equations-II

Oscillatory and asymptotic behaviour of solutions of a class of fourth order nonlinear neutral difference equations of the form

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

NONOSCILLATION AT A FINITE POINT FOR LINEAR HAMILTONIAN SYSTEM

Using the associated quadratic functional of the Hamiltonian system, we obtain the non-oscillation of all the prepared solutions for the Hamiltonian system at a finite point.     

Non-oscillation Criteria for Hypoelastic Models under Simple Shear Deformation

Ten objective rates, spinning or non-spinning, are critically examined from the viewpoint of Sturm's theorems in ordinary differential equations. Upon developing implication relations of oscillatory, non-oscillatory, and disconjugate behavior, we establish oscillation and non-oscillation criteria which pick out the objective stress rates that lead to oscillatory and non-oscillatory responses in simple shear deformation, respectively. Among the hypoelastic equations associated with the spinning objective rates examined, the Jaumann equation is an oscillatory minorant, the homogeneous Xiao–Bruhns–Meyers equation is a non-oscillatory majorant, and the homogeneous Green–Naghdi equation is a disconjugate majorant. If (Sturm comparable) non-spinning objective rates are also taken into consideration, then the Durban–Baruch equation becomes an oscillatory minorant, but the other two equations remain to play the same roles. The Jaumann equation is a Sturm majorant for all the other nine homogeneous hypoelastic equations, and the homogeneous Szabó–Balla-2 equation is a Sturm minorant for all the other nine homogeneous hypoelastic equations. Most of the solutions of the zeroth-grade hypoelastic equations at simple shear have already been published, except for those of Szabó and Balla, to which the closed-form solutions are derived here. Moreover, all solutions are extended to include the effect of initial stresses. This revised version was published online in August 2006 with corrections to the Cover Date.     

COMPARISON THEOREMS AND OSCILLATION CRITERIA FOR DIFFERENCE EQUATIONS WITH SEVERAL DELAYS

In this paper, we first establish the equivalence of the oscillation of thedifference equations with several delays of the form: Δx_n+sum from i=1 to m(pi(n)x_(n-k_i))=0 for n≥0and the second-order difference equations without delay of the form:where{pj(n)}is a sequence of nonnegative real numbers and{k_i}_(i=1)~m is a setof positive integers. Then we get some "sharp" conditions for oscillation andnon-oscillation of the first equation.     

Oscillation of fourth order nonlinear neutral difference equations I

Oscillatory and asymptotic behaviour of solutions of a class of nonlinear fourth order neutral difference equations of the form