For my Bachelor thesis i would like to proof the following statment. Let $E$ be a Banach space and $Q\subset E$. $\alpha$ is the kuratowski measure of noncompactness.
Let $f:[0,T]\times Q\rightarrow E$ be a continous and bounded function. If there exists a $L\geq 0$ so that $$\alpha(f([0,T]\times A))\leq L\alpha(A)$$
for every bounded $A\subset Q$, then the cauchy Problem
$$x'(t)=f(t,x(t))$$ with $$ x(0)=x_0$$ has a solution.
This theorem was proofed by Szufla in S. Szufla, Some remarks on Ordinary Differential Equations in Banach Spaces, Bull. Acad. Pol. Sci., sc. math, astr., phys., 16 (1968), 795-800.
I really cant find the paper anywhere. Does someone know where I can find it or how to proof it? Thanks for your help.