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J. Korean Math. Soc. 2011; 48(6): 1143-1152
Printed November 1, 2011
https://doi.org/10.4134/JKMS.2011.48.6.1143
Copyright © The Korean Mathematical Society.
Existence of periodic solutions for planar Hamiltonian systems at resonance
Yong-In Kim
University of Ulsan
The existence of periodic solutions for the planar Hamiltonian systems with positively homogeneous Hamiltonian is discussed. The asymptotic expansion of the Poincar\'e map is calculated up to higher order and some sufficient conditions for the existence of periodic solutions are given in the case when the first order term of the Poincar\'e map is identically zero.
Keywords: planar Hamilton system, resonance, periodic solution
MSC numbers: 34A12, 34A34
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