On the existence of periodic solutions for a class of non-autonomous differential delay equations
Keywords
Hamiltonian system, Floquet theory, symplectic transformation, periodic solution, delay equation, critical point theoryAbstract
This paper considers the existence of periodic solutions for a class of non-autonomous differential delay equations $$ x'(t)=-\sum_{i=1}^{n-1}f(t,x(t-i\tau)), \leqno{(*)} $$ where $\tau> 0$ is a given constant. It is shown that under some conditions on $f$ and by using symplectic transformations, Floquet theory and some results in critical point theory, the existence of single periodic solution of the differential delay equation $(*)$ is obtained. These results generalize previous results on the cases that the equations are autonomous.Downloads
Published
2010-04-23
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CHENG, Rong, XU, Junxiang & ZHANG, Dongfebg. On the existence of periodic solutions for a class of non-autonomous differential delay equations. Topological Methods in Nonlinear Analysis [online]. 23 April 2010, T. 35, nr 1, s. 139–154. [accessed 6.2.2023].
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