Hajnosz, Andrzej On the existence of solutions of differential equations in Banach spaces. (English) Zbl 0858.34047 Zesz. Nauk. Politech. Rzesz. 121, Mat. Fiz. 18, Mat. 14, 59-88 (1993). Using the abstract concepts of the measure of noncompactness, the regularity of mappings and the Kamke comparison function, the author proves some general versions of well-known results concerning the existence and uniqueness of solutions of the Cauchy problem \(x'=f(t,x)\), \(x(0)=x_0\) in Banach spaces. Such an approach permits to unify the classical results involving compactness or dissipative conditions. Reviewer: J.Myjak (L’Aquila) MSC: 34G20 Nonlinear differential equations in abstract spaces 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations Keywords:measure of noncompactness; regularity of mappings; Kamke comparison function; existence; uniqueness; Cauchy problem; Banach spaces PDFBibTeX XMLCite \textit{A. Hajnosz}, Zesz. Nauk. Politech. Rzesz. 121, Mat. Fiz. 18, Mat. 14, Mat. Fiz. 18, Mat. 14, 59--88 (1993; Zbl 0858.34047)