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EXISTENCE OF PERIODIC SOLUTIONS FOR PLANAR HAMILTONIAN SYSTEMS AT RESONANCE

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대한수학회 (The Korean Mathematical Society)|2011.11|대한수학회지 (Journal of the KMS)|제48권 제6호|pp. 1143-1152

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참고문헌

키워드

resonanceperiodic solutionplanar Hamilton system
주제분류수학

초록

The existence of periodic solutions for the planar Hamilton-ian systems with positively homogeneous Hamiltonian is discussed. The asymptotic expansion of the Poincare map is calculated up to higher or-der and some sufficient conditions for the existence of periodic solutions are given in the case when the first order term of the Poincare map is identically zero.

Abstract

The existence of periodic solutions for the planar Hamilton-ian systems with positively homogeneous Hamiltonian is discussed. The asymptotic expansion of the Poincare map is calculated up to higher or-der and some sufficient conditions for the existence of periodic solutions are given in the case when the first order term of the Poincare map is identically zero.

참고문헌 (13)

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  8. A. Fonda, "Planar differential systems at resonance", Adv. Differential Equations, 11(10), pp.1111~1133 (2006)
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  10. J. Massera, "The existence of periodic solutions of systems of differential equations", Duke Math. J, 17, pp.457~475 (1950)
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관련 논문AI추천

A NOTE ON QUASI-PERIODIC PERTURBATIONS OF ELLIPTIC EQUILIBRIUM POINTSHouyu Zhao대한수학회 · 대한수학회보2012 · 제49권 제6호Periodic solutions for the nonlinear Hamiltonian systems정택선, 최규흥강원경기수학회 · 한국수학논문집2009 · 제17권 제3호EXISTENCE OF HOMOCLINIC ORBITS FOR LI¶ENARD TYPE SYSTEMS김용인한국수학교육학회 · 이론수학과 교직수학2010 · 제17권 제4호PERIODIC SOLUTIONS FOR A KIND OF p-LAPLACIAN HAMILTONIAN SYSTEMSLi Zhang, Weigao Ge대한수학회 · 대한수학회보2010 · 제47권 제2호Bounded weak solution for the Hamiltonian system정택선, 최규흥강원경기수학회 · 한국수학논문집2013 · 제21권 제1호Multiple periodic solutions of second-order ordinary differential equations across resonanceHua Cai, Xiaojun Chang, Xin Zhao대한수학회 · 대한수학회보2014 · 제51권 제5호

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