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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.
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참고문헌 (13)
참고문헌 신청
A. Capietto / 2003 / Periodic solutions of Lienard equations with asymmetric nonlinearities at resonance / J. London Math. Soc 68 (1) : 119 ~ 132
A. Capietto / 2008 / Coexistence of unbounded and periodic so- lutions to perturbed damped isochronous oscillators at resonance / Proc. Roy. Soc. Edin- burgh Sect. A 138 (1)
A. Fonda / 2004 / Positively homogeneous Hamiltonian systems in the plane / J. Differential Equations 200 (1) : 162 ~ 184
A. Fonda / 2006 / Planar differential systems at resonance / Adv. Differential Equations 11 (10) : 1111 ~ 1133
C. Fabry / 1998 / Nonlinear resonance in asymmetric oscillators / J. Differential Equations 147 (1) : 58 ~ 78
A. Capietto / 2008 / Coexistence of unbounded and periodic so- lutions to perturbed damped isochronous oscillators at resonance / Proc. Roy. Soc. Edin- burgh Sect. A 138 (1)
A. Fonda / 2004 / Positively homogeneous Hamiltonian systems in the plane / J. Differential Equations 200 (1) : 162 ~ 184
A. Fonda / 2006 / Planar differential systems at resonance / Adv. Differential Equations 11 (10) : 1111 ~ 1133
C. Fabry / 1998 / Nonlinear resonance in asymmetric oscillators / J. Differential Equations 147 (1) : 58 ~ 78
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