Nonlocal Cauchy problems governed by compact operator families

Abstract We study the existence of mild solutions for the nonlocal Cauchy problem u′(t)=Au(t)+f(t,u(t)), t∈[t 0 ,t 0 +T], u(t 0 )+g(u)=u 0 , and give new criterions, which extend some existing results in this area.

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