A note on weakly isotone maps and common solutions for differential systems (Q2508640)

The authors offer remarks on the existence of common solutions of the first order differential Cauchy problems studied by \textit{B.\,C.\,Dhage} [Bull.\ Korean Math.\ Soc.\ 36, No.\,3, 565--578 (1999; Zbl 0940.47043)], \textit{B.\,C.\,Dhage, S.\,Heikkilä} and \textit{M. \,Kumpulainen} [Indian J.\ Pure Appl.\ Math. 26, No.\,5, 411--416 (1995; Zbl 0839.47035)], \textit{H.\,K.\,Pathak} [Riv.\ Mat.\ Univ.\ Parma, V.\,Ser.\ 3, 193--202 (1994; Zbl 0876.47032)] and the reviewer [Riv.\ Mat.\ Univ.\ Parma. IV.\,Ser.\ 16, 205--212 (1990; Zbl 0725.45013)]. They conclude that some of the fundamental hypotheses used by them are too strong to obtain interesting results for common solutions of differential systems in the space \(\mathbb R^n\).