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In this work we give a new criteria for the existence of periodic and almost periodic solutions for some dieren tial equation in a Banach space. The linear part is nondensely dened and satises the Hille-Yosida condition. We prove the existence of periodic and almost periodic solutions with condition that is more general than the known exponential dichotomy. We apply the new criteria for the existence of periodic and almost periodic solutions for some partial functional dieren tial equation whose linear part

New criteria for the existence of periodic and almost periodic solutions for some evolution equations in Banach spaces