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Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem. (English) Zbl 0748.34040
Theorem on existence and uniqueness for semilinear evolution equations in Banach spaces are given. The problem is a “nonlocal” one, i.e., a relation between the solution values at different time-points is given. The theory of semigroups of linear operators is the main tool used.

MSC:
34G20 Nonlinear differential equations in abstract spaces
47D06 One-parameter semigroups and linear evolution equations
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