Example 2. Consider the following differential equation where { t$_{n}$ } ∞ n =1 is an increasing sequence such that lim n $_{→∞}$t$_{n}$ = ∞ . It is clear that a ( t ) = 1 , b ( t ) = π, c ( t ) = e $^{t}$, τ = 5 2 and b$_{n}$ = − 2 $^{n}$. It can be shown that the hypotheses of Theorem 2 as well as Theorem 3 are satisfied. So, all solutions of Eq. (32) are oscillatory. 17 [6] A.R. Aftabizadeh, J. Wiener and J.Ming Xu, Oscillatory and periodic solutions of delay differential equations with piecewise constant argument. Proc. of Amer- ican Math. Soc. , 99 (1987) 673-679. [5] A.R. Aftabizadeh and J. Wiener, Oscillatory properties of first order linear func- tional differential equations. Applicable Anal., 20 (1985) 165-187. [4] K.L. Cooke and J. Wiener, Retarded differential equations with piecewise con- stant delays. J. Math. Anal. Appl ., 99 (1984) 265-297. [3] L. Dai and M.C. Singh, An analytical and numerical method for solving linear and nonlinear vibration problems. Int. J. Solids Struct. 34 (1997) 2709-2731. [2] L. Dai and M.C. Singh, On oscillatory motion of spring mass systems subject to piesewise constant forces. J. Sound Vib., 173 (1994) 217-233. [1] S. Busenberg and K.L. Cooke. Models of vertically transmitted diseases with sequential-continuous dynamics. In: Nonlinear Phenomena in Mathematical Sci- ences, V. Lakshmikantham (Ed.), Academic Press, (1982) 179-187. References     x $^{′}$( t ) + x ( t ) + πx ( t − 5 2 ) + e $^{t}$x ([ t − 1]) = 0 , t = t$_{n}$, n = 1 , 2 , ..., t > 0 , x ( t + $_{n}$) − x ( t − $_{n}$) = − 2 $^{n}$x ( t + $_{n}$) , n = 1 , 2 , ..., (32)