## Second-order neutral delay-differential equations with piecewise constant time dependence.(English)Zbl 1035.34093

The author establishes conditions for the existence and uniqueness of almost-periodic solutions to second-order neutral delay-differential equations with almost-periodic time dependence of the form $(x(t)+px(t-1))''=qx([t])+f(t),$ where $$[\, \cdot \,]$$ is the greatest integer function, $$p$$ and $$q$$ are nonzero constants, and $$f$$ is Bohr almost-periodic.

### MSC:

 34K40 Neutral functional-differential equations
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### References:

 [1] Cooke, K.L.; Wiener, J., A survey of differential equations with piecewise continuous arguments, (), 1-15 · Zbl 0737.34045 [2] Fink, A.M., Almost periodic differential equations, Lecture notes in math., 377, (1974), Springer-Verlag Berlin · Zbl 0325.34039 [3] Hale, J.K., Theory of functional differential equations, Appl. math. sci., 3, (1977), Springer-Verlag New York [4] Li, Z.; He, M., The existence of almost periodic solutions of second-order neutral differential equations with piecewise constant argument, Northeast. math. J., 15, 3, 369-378, (1999) · Zbl 1018.34064 [5] Yuan, R., The existence of almost periodic solutions to two-dimensional neutral differential equations with piecewise constant argument, Sci. sinica A, 27, 10, 873-881, (1997) [6] Yuan, R., A new almost periodic type of solutions of second-order neutral delay differential equations with piecewise constant argument, Sci. China, 43, 4, 371-383, (2000) · Zbl 0961.34062 [7] Zhang, C., Pseudo almost periodic solutions of some differential equations, J. math. anal. appl., 181, 62-76, (1994) · Zbl 0796.34029
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