Related papers: Iterative oscillation tests for differential equat…
We consider difference equations with several non-monotone deviating arguments and nonnegative coefficients. The deviations (delays and advances) are, generally, unbounded. Sufficient oscillation conditions are obtained in an explicit…
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…
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)) -…
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…
Consider the first-order linear differential equation with several retarded arguments $$ x^{\prime}(t)+\sum\limits_{i=1}^{m}p_{i}(t)x(\tau_{i}(t))=0,\;\;\;t\geq t_{0}, $$ where the functions $p_{i},\tau_{i}\in…
We present new criteria for the existence of oscillatory and nonoscillatory solutions of measure delay differential equations with impulses. We deal with the integral forms of the differential equations using the Perron and the…
The well established monotone iterative technique that is used to study the existence and uniqueness of fractional impulsive system is extended to Hilfer fractional order in this paper. The results are derived by using the method of upper…
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.
In the present study we highlight some results related to the oscillation for high order nonlinear generalized neutral difference equation in the following form \begin{equation*}…
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…
In this paper, we consider the solvability of a class of nonlinear fourth order integro-differential equations with Navier boundary condition. We first deal with a corresponding linear problem and establish a maximum principle. Using the…
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…
In this paper, we study both the oscillation and the stability of impulsive differential equations when not only the continuous argument but also the impulse condition involves delay. The results obtained in the present paper improve and…
We consider the anharmonic oscillator with an arbitrary-degree anharmonicity, a damping term and a forcing term, all coefficients being time-dependent: u" + g_1(x) u' + g_2(x) u + g_3(x) u^n + g_4(x) = 0, n real. Its physical applications…
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…
This paper systematically treats the asymptotic behavior of many (linear/nonlinear) classes of higher-order fractional differential equations with multiple terms. To do this, we utilize the characteristics of Caputo fractional…
The theme of this article is to provide some sufficient conditions for the asymptotic property and oscillation of all solutions of third-order half-linear differential equations with advanced argument of the form…
We prove existence of solutions for a nonlinear fractional oscillator equation with both left Riemann-Liouville and right Caputo fractional derivatives subject to natural boundary conditions. The proof is based on a transformation of the…
We provide explicit conditions for uniform stability, global asymptotic stability and uniform exponential stability for dynamic equations with a single delay and a nonnegative coefficient. Some examples on nonstandard time scales are also…
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.…