where g(t,x(t)) may be unbounded as x → 0+. Equation (1.1) is of repulsive type (resp. attractive type) if g(t,x(t))→ –∞ (resp. g(t,x(t))→ +∞) as x→ 0+. Using Mawhin’s continuation theorem, the author proved that Eq. (1.1) has at least one T-periodic solution. Zhang’s work has attracted much attention of many specialists in differential equations. In 2014,Wang [2] investigated the existence of ...

The main goal of our paper is to obtain sufficient conditions for the asymptotic equivalence a linear differential system and quasilinear impulsive equations with piecewise constant argument generalized type, in short IDEPCAG. A deviating advanced delayed type. As an auxiliary result, structure set solutions specified. Several examples are also given show feasibility results.

It is well known that time delays exist widely in biology, neural network, automatic control engineering and so on. Since the existence of delays is frequently a source of instability, bifurcation and chaos, it is important to study the dynamical behaviors of the differential equations with delays. Recently, the periodic problem of Rayleigh equations with a deviating argument x′′ + f(x′(t)) + g...