Oscillation of neutral delay difference equations of second order with positive and negative coefficients

This paper is concerned with a class of neutral difference equations of second order with positive and negative coefficients of the forms

The impact of unbounded swings of the forcing term on the asymptotic behavior of functional equations

Necessary and sufficient conditions have been found to force all solutions of the equation

On the oscillation of functional differential equations

In this paper we present certain criteria for the oscillation of functional differential equations of the form where δ = ±1, p, g: [t₀, ∞) → IR, H: [t₀,∞) × IR → IR are continuous, p(t) ≥ 0 for t ≥ t₀ and lim_t → ∞ g(t) — ∞. We like to point out that condition of the form will not be employed.     

On oscillation and nonoscillation of general functional differential equations

Oscillation and nonoscillation criteria for the nth order nonlinear functional differential equation L_nx(t) + f(t, x(t), x[g(t)]) = h(t) are established. Some illustrative examples are also included.     

Comparison theorems for noncanonical third order nonlinear differential equations

The aim of our paper is to study oscillatory and asymptotic properties of solutions of nonlinear differential equations of the third order with quasiderivatives. We prove comparison theorems on property A between linear and nonlinear equations. Some integral criteria ensuring property A for nonlinear equations are also given. Our assumptions on the nonlinearity of f are restricted to its behavior only in a neighborhood of zero and a neighborhood of infinity.      

Improved iterative oscillation tests in difference equations with several arguments

An iterative procedure is used to establish the oscillatory sufficient conditions of first-order linear difference equations with several non-monotone deviating arguments and nonnegative coefficients. The conditions obtained by this method, achieve a marked improvement on all known conditions in the literature.     

On oscillation and nonoscillation of second-order dynamic equations

New oscillation and nonoscillation criteria are established for second-order linear equations with damping and forcing terms. Examples are given to illustrate the results.     

Oscillation of nonlinear differential systems with retarded arguments

In this work we investigate some oscillatory properties of solutions of non-linear differential systems with retarded arguments. We consider the system of the form

On the Oscillation of the Fourth Order Differential Equations

61.IntroductionWeconsiderthefourthorderdifferentialequationx(`)(t)-p(t)lx(t)I'sgnx(t)=O,(1.l)wherea>l,isconstant,andp(t)ispositivecontinuousfunctionon[t,,oo),to>o.Werestrictourattentiontothosenontrivialsolutionsx(t)of(1.1)whichexistonsomehalf-[ine[T:,co)cy[t,,oo),suchasolutioniscalledapropersolutionof(1.l).ApropersolutioniscalledoscillatoryifithasarbitrarilylargezerosFotherwiseitiscallednonoscillatory.Wecon-sidertheoscillationandnonoscillationofpropersolutionsof(l,l).WeletEdenotethesetofall…     

On oscillation and nonoscillation properties of Emden-Fowler difference equations

A characterization of oscillation and nonoscillation of the Emden-Fowler difference equation

Oscillatory properties of solutions of three-dimensional differential systems of neutral type

The purpose of this paper is to obtain oscillation criteria for the differential system

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.     

广义典型流形的实例构作

陈述了广义典型流形(或拓扑域流形)的概念,并构作了拓扑域流形的若干实例,丰富了这类流形的内容,也给今后研究和运用拓扑域流形提供一些参考.     

Oscillation and Nonoscillation Criteria for Two-Dimensional Systems of First Order Linear Ordinary Differential Equations

Sufficient conditions are established for the oscillation and nonoscillation of the system     

On a certain canonical form

We amplify the well-known result due to Dlab and Ringel on the reduction of a real rectangular matrix to canonical form by formally complex transformations of rows and columns. Translated fromMatematicheskie Zametki, Vol. 67, No. 4, pp. 514–519, April, 2000.     

Canonical varieties with no canonical axiomatisation

We give a simple example of a variety of modal algebras that is canonical but cannot be axiomatised by canonical equations or first-order sentences. We then show that the variety of representable relation algebras, although canonical, has no canonical axiomatisation. Indeed, we show that every axiomatisation of these varieties involves infinitely many non-canonical sentences.

Using probabilistic methods of Erdos, we construct an infinite sequence of finite graphs with arbitrarily large chromatic number, such that each is a bounded morphic image of and has no odd cycles of length at most . The inverse limit of the sequence is a graph with no odd cycles, and hence is 2-colourable. It follows that a modal algebra (respectively, a relation algebra) obtained from the satisfies arbitrarily many axioms from a certain axiomatisation of , while its canonical extension satisfies only a bounded number of them. First-order compactness will now establish that has no canonical axiomatisation. A variant of this argument shows that all axiomatisations of these classes have infinitely many non-canonical sentences.