Existence of periodic solutions of planar systems with four delays
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Abstract
The sufficient condition for the existence of non-constant periodic solutions of the following planar system with four delays are obtained: \(\left\{ \begin{gathered} x_1^\prime \left( t \right) = - a_0 x_1^\alpha \left( t \right) + a_1 f_1 (x_1 \left( {t - \tau _1 } \right),x_2 \left( {t - \tau _2 } \right)), \hfill \\ x_2^\prime \left( t \right) = - b_0 x_2^\alpha \left( t \right) + b_1 f_2 (x_1 \left( {t - \tau _3 } \right),x_2 \left( {t - \tau _4 } \right)). \hfill \\ \end{gathered} \right.\) This approach is based on the continuation theorem of the coincidence degree, and the a-priori estimate of periodic solutions.
Subject Classification
34K13Keywords
Planar systems non-constant periodic solutions coincidence degree the a-priori estimatePreview
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© Editorial Committee of Applied Mathematics-A Journal of Chinese Universities 2001