Gatsori, E.; Ntouyas, S. K.; Sficas, Y. G. On a nonlocal Cauchy problem for differential inclusions. (English) Zbl 1080.34005 Abstr. Appl. Anal. 2004, No. 5, 425-434 (2004). The paper concerns a system which consists of the differential inclusion \[ y'(t)\in F(t,y(t)) \] and the nonlocal condition \[ y(0)+\sum_{k=1}^{p}c_ky(t_k)=y_0. \] Here, \(F:[0,b]\times \mathbb{R}^n\to \mathbb{R}^n\) is a certain Carathéodory multi-valued map, whereas \(0\leq t_1<\cdots<t_p\leq b\) and \(c_1\neq0\), …, \(c_p\neq0\). In contrast with the paper by M. Benchohra and S. K. Ntouyas [Georgian Math. J. 7, 221–230 (2000; Zbl 0960.34049)], the \(F\)-values are not necessarily convex. Using either the Covitz-Nadler fixed-point theorem or the Bressan-Colombo selection theorem combined with Schaefer’s fixed-point theorem, there are derived two distinct results which state the existence of solutions to the system above. Reviewer: Corneliu Ursescu (Iaşi) Cited in 4 Documents MSC: 34A60 Ordinary differential inclusions Keywords:differential inclusion; nonlocal Cauchy problem Citations:Zbl 0960.34049 PDFBibTeX XMLCite \textit{E. Gatsori} et al., Abstr. Appl. Anal. 2004, No. 5, 425--434 (2004; Zbl 1080.34005) Full Text: DOI EuDML