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Existence of periodic solutions of partial neutral functional differential equations with unbounded delay. (English) Zbl 0926.35151

The paper deals with the partial neutral functional differential equations with unbounded delay that can be treated in the form \[ {d\over dt}(x(t)+ F(t, x_t))= Ax(t)+ G(t, x_t),\quad t\geq 0,\tag{1} \] where \(A\) is the infinitesimal generator of a strongly continuous semigroup on a Banach space \(X\), and \(\dot F\) and \(G\) are functions satisfying certain conditions. The authors prove existence of periodic solutions of (1). The approach used in the paper is based on Sadovskij’s theorem.
Reviewer: D.Bainov (Sofia)

MSC:

35R10 Partial functional-differential equations
34K30 Functional-differential equations in abstract spaces
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