Geodesic
Existence of solutions of perturbed O.D.E.'s in Banach spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) no. 3, pp. 463-470.

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We consider a perturbed Cauchy problem like the following $$ {\hbox{\rm (PCP)}} \cases x' = A(t,x) +B(t,x) \ x(0)=x_0 \endcases $$ and we present two results showing that (PCP) has a solution. In some cases, our theorems are more general than the previous ones obtained by other authors (see [4], [8], [9], [11], [13], [17], [18]).
Classification : 34A12, 34G05, 34G20, 47H15, 47N20
Keywords: perturbed Cauchy problem; semi-inner product; measure of noncompactness 
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     author = {Emmanuele, Giovanni},
     title = {Existence of solutions of perturbed {O.D.E.'s} in {Banach} spaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
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Emmanuele, Giovanni. Existence of solutions of perturbed O.D.E.'s in Banach spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) no. 3, pp. 463-470. http://geodesic.mathdoc.fr/item/CMUC_1991__32_3_a7/