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Periodic solutions for a neutral functional differential equation with
multiple variable lags

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*Cheng-jun Guo, Gen-qiang Wang,Sui Sun Cheng*

**Address.**

Guangdong Technical College of Water Conservancy and Electric Engineering,
Guangzhou, Guangdong 510610 P. R. China

Department of Computer Science,
Guangdong Polytechnic Normal University,
Guangzhou, Guangdong 510665, P. R. China

Department of Mathematics, Tsing Hua University,
Hsinchu, Taiwan 30043, R. O. China

**E-mail. **sscheng@math.nthu.edu.tw

**Abstract.**

By means of the Krasnoselskii fixed piont theorem, periodic solutions are
found for a neutral type delay differential system of the form
\[
x^{\prime }\left( t\right) +cx^{\prime }\left( t-\tau \right) =A\left(
t,x(t)\right) x\left( t\right) +f\left( t,x\left( t-r_{1}\left( t\right)
\right) ,\dots,x\left( t-r_{k}\left( t\right) \right) \right) .
\]

**AMSclassification. ** 39A11.

**Keywords. ** Neutral differential system, periodic solutions, fixed point
theorem.