Geodesic
Periodic solutions for a neutral functional differential equation with multiple variable lags
Archivum mathematicum, Tome 42 (2006) no. 1, pp. 1-10
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By means of the Krasnoselskii fixed piont theorem, periodic solutions are found for a neutral type delay differential system of the form \[ x^{\prime }\left( t\right) +cx^{\prime }\left( t-\tau \right) =A\left( t,x(t)\right) x\left( t\right) +f\left( t,x\left( t-r_{1}\left( t\right) \right) ,\dots ,x\left( t-r_{k}\left( t\right) \right) \right) . \]
By means of the Krasnoselskii fixed piont theorem, periodic solutions are found for a neutral type delay differential system of the form \[ x^{\prime }\left( t\right) +cx^{\prime }\left( t-\tau \right) =A\left( t,x(t)\right) x\left( t\right) +f\left( t,x\left( t-r_{1}\left( t\right) \right) ,\dots ,x\left( t-r_{k}\left( t\right) \right) \right) . \]
Classification : 34K13, 47H10, 47N20
Keywords: neutral differential system; periodic solutions; fixed point theorem 
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Guo, Cheng-Jun; Wang, Gen-Qiang; Cheng, Sui-Sun. Periodic solutions for a neutral functional differential equation with multiple variable lags. Archivum mathematicum, Tome 42 (2006) no. 1, pp. 1-10. http://geodesic.mathdoc.fr/item/ARM_2006_42_1_a0/

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