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Ergodic solutions via ergodic sequences. (English) Zbl 0957.34054
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.

MSC:
34F05ODE with randomness
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Full Text: DOI
References:
[1] Alonso, A. I.; Hong, J.; Obaya, R.: Almost periodic type solutions of differential equations with piecewise constant argument via almost periodic type sequences. Appl. math. Lett. (1998) · Zbl 0978.34039
[2] Dads, E. Ait; Arino, O.: Exponential dichotomy and existence of pseudo almost periodic solutions of some differential equations. Nonlinear anal. TMA 27, No. 4, 369-386 (1996) · Zbl 0855.34055
[3] Dads, E. Ait; Ezzinbi, K.; Arino, O.: Pseudo almost periodic solutions for some differential equations in a Banach space. Nonlinear anal. TMA 28, No. 7, 1141-1155 (1997) · Zbl 0874.34041
[4] Basit, B.; Zhang, C.: New almost periodic type functions and solutions of differential equations. Can. J. Math. 48, No. 6, 1138-1153 (1996) · Zbl 0880.43009
[5] Corduneanu, C.: Almost periodic functions. (1989) · Zbl 0672.42008
[6] Fink, A. M.: Almost periodic differential equations. Lecture notes in mathematics 377 (1974) · Zbl 0325.34039
[7] Haaser, N. B.; Sullivan, J. A.: Real analysis. (1971) · Zbl 0213.33801
[8] Hale, J. K.: 2nd edition ordinary differential equations. Ordinary differential equations (1980)
[9] Halmos, P. R.: Measure theory. (1974) · Zbl 0283.28001
[10] Hong, J.; Obaya, R.; Sanz, A.: Exponential trichotomy and a class of ergodic solutions of differential equations with ergodic perturbations. Appl. math. Lett. 12, 7-13 (1999) · Zbl 0935.34044
[11] J. Hong, R. Obaya, A. Sanz, Almost periodic type solutions of some differential equations with piecewise constant arguments, Nonlinear Anal. TMA, in press. · Zbl 0996.34062
[12] Meisters, G. H.: On almost periodic solutions of a class of differential equations. Proc. amer. Math. soc. 10, 113-119 (1959) · Zbl 0092.30401
[13] Nemytskii, V.; Stepanoff, V.: Qualitative theory of differential equations. (1960) · Zbl 0089.29502
[14] Opial, Z.: Sur LES solutions presque-periodiques d’une classe d’equations differentielles. Ann. polon. Math. 9, 157-181 (1960/61)
[15] Zhang, C.: Pseudo almost-periodic solutions of some differential equations. J. math. Anal. appl. 181, 62-76 (1994) · Zbl 0796.34029
[16] Zhang, C.: Integration of vector-valued pseudo-almost periodic functions. Proc. amer. Math. soc. 121, 167-174 (1994) · Zbl 0818.42003