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The existence of almost-periodic solutions to second-order neutral differential equations with piecewise constant argument. (English) Zbl 1018.34064

Summary: The authors consider the following neutral functional-differential equations with piecewise constant argument \[ \begin{aligned} &{d^2\over dt^2} (x(t)+ px(t- 1))= qx\Biggl(2\Biggl[{t+1\over 2}\Biggr]\Biggr)+ g(t, x(t), x([t])),\quad\text{or}\\ & {d^2\over dt^2} (x(t)+ p(t) x(t-1))= qx\Biggl(2\Biggl[{t+ 1\over 2}\Biggr]\Biggr)+ g(t, x(t), x([t])).\end{aligned} \] Constructing an almost-periodic solution to some difference equation and using a fixed-point theorem, they obtain the existence of almost-periodic solutions to these equations.

MSC:

34K14 Almost and pseudo-almost periodic solutions to functional-differential equations
34K40 Neutral functional-differential equations
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