Related papers: A simple oscillation criteria for second-order dif…
The Riccati equation method is used to establish oscillation and non-oscillation criteria for second order linear nonhomogeneous functional-differential equations.We show that the obtained oscillation criterion is a generalization of J. S.…
Some properties of global solution of scalar Riccati equation are studied. On the basis of these properties using the Whiburn's and Leighton - Nehary's theorems some oscillatory and criteria are proved for second order linear systems of…
The Riccati equation method is used to establish an oscillatory and a non oscillatory criteria for nonhomogeneous linear systems of two first-order ordinary differential equations. It is shown that the obtained oscillatory criterion is a…
The Riccati equation method is used to establish some oscillatory criteria for the second order linear functional - differential equations of multiple terms with locally integrable coefficients. An interval oscillation criterion for the…
In this paper we use the Riccati equation method with other ones to establish global solvability, stability and oscillation criteria for a class of two dimensional nonlinear systems of ordinary differential equations, which is a…
The Riccati equation method is used to establish three new oscillatory criteria for the second order linear ordinary differential equations in the marginal, sub extremal and extremal cases.We show that the first of these criteria implies…
A class of first order linear impulsive differential equation with continuous and piecewise constant arguments is studied. Sufficient conditions for the oscillation of the solutions are obtained.
We give some sufficient conditions that ensure oscillations and nonoscillations for nonautonomous impulsive differential equations with piecewise constant arguments of generalized type. We cover several cases of differential equations with…
This paper studies the oscillatory behavior of solutions to linear nonautonomous impulsive differential equations with piecewise constant arguments, including both advanced and delayed cases \[ x'(t) = a(t)x(t) + b(t)x([t-k]), \quad k \in…
The Riccati equation method is used to establish some global solvability criteria for some classes of second order nonlinear ordinary differential equations. Two oscillation theorems are proved. The results are applied to the Emden - Fowler…
The Riccati equation method is used for study the oscillatory and non oscillatory behavior of solutions of systems of two first order linear two by two dimensional matrix differential equations. An integral and an interval oscillatory…
This paper extends the discriminant associated to second order linear constant coefficient differential equations to general second order linear differential equations. The main result of this paper is that the discriminant of a second…
The Riccati equation method and an approach of the use of unknown factors is used to establish oscillation, suboscillation and nonoscillation criteria for linear systems of ordinary differential equations. A necessary condition for Lyapunov…
A class of fourth--order neutral type difference equations with quasidifferences and deviating arguments is considered. Our approach is based on studying the considered equation as a system of a four--dimensional difference system. The…
The oscillatory behavior of the solutions to a differential equation with several non-monotone delay arguments and non-negative coefficients is studied. A new sufficient oscillation condition, involving lim sup, is obtained. An example…
The goal of our work is to investigate the oscillation and asymptotic properties of a class of difference equations with a condition. In contrast to most previous studies, the oscillation of the investigated equation is obtained with only…
Ordinary differential equations of the second order with one constant delay are considered in this paper. An analytical representation of the solution is obtained using the method of steps.
It is well known that second order linear ordinary differential equations with slowly varying coefficients admit slowly varying phase functions. This observation is the basis of the Liouville-Green method and many other techniques for the…
In this article we study solutions to second order linear difference equations with variable coefficients. Under mild conditions we provide closed form solutions using finite continued fraction representations. The proof of the results are…
We provide sufficient criteria for the oscillation of all solutions of neutral delay differential equations of the form \[ \left[x(t) - \sum_{i=1}^{N_r}R_i(t)x(t - r_i(t)) \right]' + \sum_{i=1}^{N_p}P_i(t)x(t - \tau_i(t)) -…