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Bull. Korean Math. Soc. 2014; 51(5): 1433-1451
Printed September 30, 2014
https://doi.org/10.4134/BKMS.2014.51.5.1433
Copyright © The Korean Mathematical Society.
Multiple periodic solutions of second-order ordinary differential equations across resonance
Hua Cai, Xiaojun Chang, and Xin Zhao
Jilin University, Jilin University, Jilin Agricultural University
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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