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Zbl 0957.34054
Hong, Jialin; Obaya, Rafael; Sanz, Ana M.
Ergodic solutions via ergodic sequences. (English)
[J] Nonlinear Anal., Theory Methods Appl. 40, No.1-8, A, 265-277 (2000). ISSN 0362-546X

It is known (G. H.~Meisters, Z.~Opial, and A. M.~Fink) that the existence of almost-periodic solutions to ordinary differential equations is equivalent to the fact that the restriction of a bounded solution to some discrete subgroup of reals is almost-periodic. There are results of this kind [see, e.g., {\it A. I.~Alonso, J.~Hong} and {\it R.~Obaya}, Almost periodic type solutions of differential equations with piecewise constant argument via almost periodic type sequences, Appl. Math. Lett. 13, No. 2, 131-137 (2000)]on the existence of almost-periodic, asymptotically almost-periodic, and pseudo almost-periodic solutions to differential equations with piecewise constant argument. In the paper, a similar result on the existence of ergodic solutions is obtained under conditions similar to those of G. H.~Meisters, Z.~Opial, and A. M.~Fink.
[Eugene Ershov (St.Peterburg)]

MSC 2000:: *34F05 ODE with randomness

Keywords: ergodic solutions; ergodic sequences; $\Cal F$-ergodicity; ordinary differential equations

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