The neutral differential equation (1.1) $$ \frac{{\mathrm{d}}^n}{{\mathrm{d}} t^n} [x(t)+x(t-\tau)] + \sigma F(t,x(g(t))) = 0, $$ is considered under the following conditions: $n\ge 2$, $\tau >0$, $\sigma = \pm 1$, $F(t,u)$ is nonnegative on $[t_0, \infty) \times (0,\infty)$ and is nondecreasing in $u\in (0,\infty)$, and $\lim g(t) = \infty$ as $t\rightarrow \infty$. It is shown that equation (1.1) has a solution $x(t)$ such that (1.2) $$ \lim_{t\rightarrow \infty} \frac{x(t)}{t^k}\ \text{exists and is a positive finite value if and only if} \int^{\infty}_{t_0} t^{n-k-1} F(t,c[g(t)]^k){\mathrm{d}} t < \infty\text{ for some }c > 0. $$ Here, $k$ is an integer with $0\le k \le n-1$. To prove the existence of a solution $x(t)$ satisfying (1.2), the Schauder-Tychonoff fixed point theorem is used.
Does there exist an atomic lattice effect algebra with non-atomic subalgebra of sharp elements? An affirmative answer to this question (and slightly more) is given: An example of an atomic MV-effect algebra with a non-atomic Boolean subalgebra of sharp or central elements is presented.