Multiplicity Results on Period Solutions to Higher Dimensional Differential Equations with Multiple Delays

作者：Guo, Zhiming; Yu, Jianshe^*

来源：Journal of Dynamics and Differential Equations, 2011, 23(4): 1029-1052.

DOI：10.1007/s10884-011-9228-z

• Period solution
• Higher dimensional differential equations
• Multiple delays
• S-1 geometrical pseudo index theory
• Critical point theory

This paper deals with the existence and multiplicity of periodic solutions to delay differential equations of the form
(z) over dot(t) = -f(z(t - 1)) - f(z(t - 2)) - ... - f(z(t - 2n + 1))
where z is an element of R-N, f is an element of C(R-N,R-N). By using the S-1 pseudo geometrical index theory in the critical point theory, some known results for Kaplan-Yorke type differential delay equations are generalized to higher dimensional case. As a result, the Kaplan-Yorke's conjecture is proved to be true in the case of higher dimensional systems.

• 出版日期2011-12
• 单位广州大学