We prove that the Picard-Lindelöf operator
with a vector function is continuous and compact (condensing) in , if satisfies only a mild boundedness condition, and if is continuous and compact (resp. condensing). This generalizes recent results of the second author and immediately leads to existence theorems for local weak solutions of the initial value problem for ordinary differential equations in Banach spaces.
Cite this article
Jürgen Appell, Martin Väth, A. Vignoli, Compactness and Existence Results for Ordinary Differential Equations in Banach Spaces. Z. Anal. Anwend. 18 (1999), no. 3, pp. 569–584DOI 10.4171/ZAA/899