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\iteman{io-port 05807320}
\itemau{Huang, Zhenkun; Wang, Xinghua; Xia, Yonghui}
\itemti{A topological approach to the existence of solutions for nonlinear differential equations with piecewise constant argument.}
\itemso{Chaos Solitons Fractals 39, No. 3, 1121-1131 (2009).}
\itemab
Summary: We investigate qualitative behavior of nonlinear differential equations with piecewise constant argument (PCA). A topological approach of Wa\D{z}ewski-type which gives sufficient conditions to guarantee that the graph of at least one solution stays in a given domain is formulated. Moreover, our results are also suitable for a class of general system of discrete equations. By using a regular polyfacial set, we apply our developed topological approach to cellular neural networks (CNNs) with PCA. Some new results are attained to reveal dynamic behavior of CNNs with PCA and discrete-time CNNs. Finally, an illustrative example of CNNs with PCA shows usefulness and effectiveness of our results. Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.
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\itemli{doi:10.1016/j.chaos.2007.04.029}
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