ON NONLOCAL EVOLUTION FUNCTIONAL-DIFFERENTIAL PROBLEM IN A BANACH SPACE

Ludwik Byszewski,

Teresa Winiarska

Abstrakt

The aim of this paper is to prove two theorems on the existence and uniqueness of mild and classical solutions of a nonlocal semilinear functional-differential evolution Cauchy problem in a Banach space. The method of semigroups, the Banach fixed-point theorem and the Bochenek theorem (see [3]) about the existence and uniqueness of the classical solution of the first order differential evolution problem in a not necessarily reflexive Banach space are used to prove the existence and uniqueness of the solutions of the considered problem. The results are based on publications [1 — 8].

Słowa kluczowe: evolution problem, functional-differential problem, nonlocal problem
References

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