Multiple periodic solutions of second-order ordinary differential equations across resonance
Bull. Korean Math. Soc. 2014 Vol. 51, No. 5, 1433-1451
https://doi.org/10.4134/BKMS.2014.51.5.1433
Printed September 30, 2014
Hua Cai, Xiaojun Chang, and Xin Zhao
Jilin University, Jilin University, Jilin Agricultural University
Abstract : In this paper we study the existence of multiple periodic solutions of second-order ordinary differential equations. New results of multiplicity of periodic solutions are obtained when the nonlinearity may cross multiple consecutive eigenvalues. The arguments are proceeded by a combination of variational and degree theoretic methods.
Keywords : periodic solutions, ordinary differential equations, resonance, variational method, Leray-Schauder degree
MSC numbers : 34C25, 58E30
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