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\title{Simple Article For AMEN\thanks{%
Mathematics Subject Classifications: 35C20, 35D10.}}
\date{{\small 20 July 2000}}
\author{First Second Family\thanks{%
Department of Mathematics, Binzhou Normal College, Binzhou, Shandong 256604,
P. R. China}\ , Sui Sun Cheng\thanks{%
Department of Mathematics, Tsing Hua University, Hsinchu, Taiwan 30043, R.
O. China}\ , Tzon Tzer Lu\thanks{%
Department of Applied Mathematics, Sun Yat-sen Univeristy, Kaohsiung, Taiwan
80424, R. O. China}}
\maketitle

\begin{abstract}
Solutions of the form $x(z)=\lambda z^{\mu }$ are found for the iterative
functional differential equation $x^{(n)}(z)=\left( x\left( x\left(
...x\left( z\right) \right) \right) \right) ^{k}.$
\end{abstract}

\section{Introduction}

The basic idea is that a short note should be presented in a simple manner.
Therefore, use simple notations, symbols, etc. Displayed equation should be
labeled in the following format 
\begin{equation}
x(z)=\lambda z^{\mu },  \label{1}
\end{equation}
\begin{equation}
x^{(n)}(z)=\left( x^{[m]}(z)\right) ^{k}.  \label{2}
\end{equation}

Lemmas, Theorems, and Corollaries should be typed such as the following:

\smallskip

THEOREM 1. Let $\Omega $ be a domain of the complex plane $C$ which does not
include the negative real axis (nor the origin). Then there exist $m$
distinct (single valued and analytic) power functions of the form (\ref{1})
which are solutions of (\ref{2}).

\smallskip

Proofs should be typed as follows:

\smallskip

PROOF. We remark that each solution $x_{i}(z)=\lambda _{i}z^{\mu _{i}}$ has
a nontrivial fixed point $\alpha _{i}$. Indeed, from $\lambda _{i}\alpha
_{i}^{\mu _{i}}=\alpha _{i},$ we find 
\[
\alpha _{i}=\lambda _{i}^{1/(1-\mu _{i})}=\left[ \mu _{i}(\mu _{i}-1)\cdot
\cdot \cdot (\mu _{i}-n+1)\right] ^{1/(k+n-1)}\neq 0, 
\]
...

\smallskip

Other texts can be typed such as the following: As an example, consider the
equation 
\[
x^{\prime }(z)=x(x(z)). 
\]
From 
\[
\mu ^{2}-\mu +1=0, 
\]
we find roots $\mu _{\pm }=(1-\sqrt{3}i)/2.$ We find $\lambda _{-}=\mu
_{-}^{1/\mu _{-}}\approx 2.145-1.238i,$ $\lambda _{+}=\mu _{+}^{1/\mu
_{+}}\approx 2.145+1.238i.$ Since $\left| \mu _{\pm }\right| =1$ and $\mu
_{\pm }^{6}=1,$ they are roots of unity. This shows that the requirements in
the main Theorem in [1] does not hold. Therefore, we have found analytic
solutions which cannot be guaranteed by the main Theorem in [1]. \smallskip

Figures should be prepared in the EPS format and placed at the center by
commands such as: centereps\{width\}\{height\}\{file\}.

\smallskip

References should be typed as follows:

\begin{thebibliography}{9}
\bibitem{r1}  J. G. Si, W. R. Li and S. S. Cheng, Analytic solutions of an
iterative functional differential equation, Computers Math. Applic.,
33(6)(1997), 47--51.

\bibitem{r2}  E. Eder, The functional differential equation $x^{\prime
}(t)=x(x(t)),$ J. Diff. Eq., 54(1984), 390--400.

\bibitem{r3}  L. W. Griffiths, Introduction to the Theory of Equations, 2$%
^{nd}$ ed., Wiley, New York, 1947.
\end{thebibliography}

\end{document}

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