Bereketoglu, H.; Seyhan, G.; Ogun, A. Advanced impulsive differential equations with piecewise constant arguments. (English) Zbl 1218.34095 Math. Model. Anal. 15, No. 2, 175-187 (2010). Differential equations with piecewise constant arguments are related to difference and differential equations. In this paper, the authors are interested in such equations with impulses. They start by proving the existence and uniqueness of solutions. Then they give necessary and sufficient conditions for the existence of periodic solutions. The paper is completed by a result on oscillations and nonoscillations and a result on the asymptotical stability of the null solution. Reviewer: Mustapha Yebdri (Tlemcen) Cited in 20 Documents MSC: 34K45 Functional-differential equations with impulses 34K11 Oscillation theory of functional-differential equations 34K25 Asymptotic theory of functional-differential equations 34K13 Periodic solutions to functional-differential equations Keywords:impulsive differential equations; piecewise constant argument; oscillation; periodicity; global asymptotic stability PDFBibTeX XMLCite \textit{H. Bereketoglu} et al., Math. Model. Anal. 15, No. 2, 175--187 (2010; Zbl 1218.34095) Full Text: DOI