Aronszajn type theorems for an mth order differential equation in Banach spaces (Q1976031)

Under a suitable condition the authors prove that the solution set to the problem \(x^{(n)} = f(t,x)\), \(n\geq 2\), is a compact \(R_{\delta}\) set in the space of all continuous functions \(x:J \to E\) endowed with the metric of uniform convergence. (Here, \(f:[0,a] \times B \to E\) is a bounded continuous function, \(E\) is a Banach space and \(J= [0,h]\) where \(h \in (0,a]\) depends on \(f\) and on the radius of \(B\)).