Oscillation of coupled nonlinear discrete systems

The problem of oscillation of a second order nonlinear difference system is considered and conditions for oscillation are derived by means of a complete analysis of nonoscillatory solutions. The case of systems with deviating arguments is also analyzed, and the results are shown to significantly generalize some existing ones.     

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

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

Global monotonicity and oscillation for second order differential equation

Oscillatory properties of the second order nonlinear equation

First order nonlinear differential inequalities with deviating arguments

Abstract. In this paper ,some new properties of solutions of the first order nonlinear differential inequalities with deviating arguments are given. These results improve many corresponding ones in the literature.     

Oscillation of first-order differential equations with retarded arguments

In this paper, we provide a test under which every solution of a first-order delay differential equation oscillates. An example is given to illustrate the significance of the result.     

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     

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 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

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…     

Oscillation for higher order superlinear delay differential equations with unstable type

We first show that the n-order superlinear delay differential equation with unstable type

     

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     

Oscillation of even order nonlinear functional differential equations with damping

This paper is concerned with a class of even order nonlinear damped differential equations

Some Oscillation Theorems for Second Order Differential Equations

In this paper we establish some oscillation or nonoscillation criteria for the second order half-linear differential equation

Positive solutions of higher-order nonlinear fractional differential systems with nonlocal boundary conditions

The paper deals with the existence and multiplicity of positive solutions for a system of higher-order nonlinear fractional differential equations with nonlocal boundary conditions. The main tool used in the proof is fixed point index theory in cone. Some limit type conditions for ensuring the existence of positive solutions are given.     

Oscillation and asymptotic behavior of third-order nonlinear neutral delay differential equations with distributed deviating arguments

This paper concerns the oscillation and asymptotic behavior of a class of third-order nonlinear neutral delay differential equations with distributed deviating arguments. By employing a generalized Riccati transformation and integral averaging technique, we establish some sufficient conditions to ensure that all solutions of the considered equations are either oscillatory or converge to zero, which extend and improve some known results in the literature.