Periodic solutions for second order periodic differential equations under scalable control

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• 作者：Shugui Kang^a ; Sui Sun Cheng^b ; ^{sscheng@math.nthu.edu.tw}
• 关键词：Second order differential equation ; Periodic solution ; Cone ; Fixed point theorem ; Existence ; Uniqueness
• 刊名：Applied Mathematics and Computation
• 出版年：2012
• 期刊代码：7_00963003
• 类别：cp
• 出版时间：15 May, 2012
• 卷：218
• 期：18
• 页码：9138-9146
• 文件大小：207 K

摘要

Second order periodic differential equations such as the Hill鈥檚 equation are used to model damped oscillators, vibrating elliptical drumheads, rotating electric dipoles, etc. and existence of periodic solutions are important. In this paper we study second order equations subject to 鈥榓djustable鈥?feedback control functions with delays. Based on the fixed point theorem for an ordered Banach space, the existence, multiplicity, and the nonexistence of periodic solutions for our equation are obtained. The uniqueness of periodic solutions and the dependence of periodic solutions on the adjustable scale factor are also studied.