Related papers: Iterative oscillation tests for difference equatio…
Sufficient oscillation conditions involving $\limsup $ and $\liminf $ for first-order differential equations with several non-monotone deviating arguments and nonnegative coefficients are obtained. The results are based on the iterative…
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 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…
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 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…
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)) -…
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…
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 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…
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…
For a nonlinear equation with several variable delays $$ \dot{x}(t)=\sum_{k=1}^m f_k(t, x(h_1(t)),\dots,x(h_l(t)))-g(t,x(t)), $$ where the functions $f_k$ increase in some variables and decrease in the others, we obtain conditions when a…
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…
We discuss alternative iteration methods for differential equations. We provide a convergence proof for exactly solvable examples and show more convenient formulas for nontrivial problems.
We obtain large and moderate deviation estimates, as well as concentration inequalities, for a class of nonuniformly expanding maps with stretched exponential decay of correlations. In the large deviation regime, we also exhibit examples…
Nonstationary and nonlinear signals are ubiquitous in real life. Their decomposition and analysis is an important topic of research in signal processing. Recently a new technique, called Iterative Filtering, has been developed with the goal…
We study limit cycles of nonlinear oscillators described by the equation $\ddot x + \nu F(\dot x) + x =0$. Depending on the nonlinearity this equation may exhibit different number of limit cycles. We show that limit cycles correspond to…
By topological arguments, we prove new results on the existence, non-existence, localization and multiplicity of nontrivial solutions of a class of perturbed nonlinear integral equations. These type of integral equations arise, for example,…
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…
A nonlinear stochastic differential equation with the order of nonlinearity higher than one, with several discrete and distributed delays and time varying coefficients is considered. It is shown that the sufficient conditions for…
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*}…