Abstract:We consider a perturbed Cauchy problem like the following $$ {\text {(PCP)}} \cases x' = A(t,x) +B(t,x) x(0)=x_0 \endcases $$ 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]).
Keywords: perturbed Cauchy problem, semi-inner product, measure of noncompactness
AMS Subject Classification: 34G05, 34G20