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Article

Keywords:
existence; bounded solutions; quasilinear differential; trichotomy; measures of noncompactness; Banach spaces
Summary:
The existence of bounded solutions for equations $x'=A(t)x+f(t,x)$ in Banach spaces is proved. We assume that the linear part is trichotomic and the perturbation $f$ satisfies some conditions expressed in terms of measures of noncompactness.
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