In the paper, shunting inhibitory cellular neural networks with impulses and the generalized
piecewise constant argument are under discussion. The main modeling novelty is that the …

It is well known that differential equations with piecewise constant arguments is a class of
functional differential equations, which has fascinated many scholars in recent years. These …

In this paper, ordinary and exponential dichotomies are defined in differential equations with
equations with piecewise constant argument of general type. We prove the asymptotic …

We obtain sufficient conditions for the existence of a uniformly and Hölder continuous
homeomorphism between the solutions of a linear differential system with piecewise …

This book is devoted to bifurcation theory in discontinuous dynamical systems. The main
novelty is the consideration of bifurcation in differential and hybrid equations by means of …

The differential equations with piecewise constant argument (DEPCAs, for short) is a class of
hybrid dynamical systems (combining continuous and discrete). In this paper, under the …

In this work, we give a version of Grobman–Hartman theorem for the nonautonomous
differential equations with piecewise constant argument of generalized type when the …

Using Krasnoselskii's fixed point theorem and dichotomy theory, we prove the existence of
periodic solutions for differential equations with multiple delays of the form x′(t)+ cx′(t− τ) …

In this paper, we study the partial differential equation with piecewise constant argument of
the form: xt (t, s)= A (t) x (t, s)+ B (t, s) x (t, s)+ C (t, s) x (t, s)+ D (t, s) x (t, s)+ f (x (t, s)), t, s∈ …

An unpredictable solution is found for a quasilinear differential equation with generalized
piecewise constant argument (EPCAG). Sufficient conditions are provided for the existence …