Positively homogeneous hamiltonian systems in the plane

被引:42
作者
Fonda, A [1 ]
机构
[1] Univ Trieste, Dipartimento Sci Mat, I-34127 Trieste, Italy
关键词
periodic; bounded and unbounded solutions; Hamiltonian systems;
D O I
10.1016/j.jde.2004.02.001
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
I try to give a general description of the dynamics of the solutions for a planar hamiltonian svstem with positively homogeneous hanliltonian function and periodic forcing term. Most of the results obtained are already known in the special case of a scalar second-ordcr differential equations with asymmetric nonlinearity. (C) 2004 Elsevier Inc. All rights reserved.
引用
收藏
页码:162 / 184
页数:23
相关论文
共 21 条
[1]   Roots of unity and unbounded motions of an asymmetric oscillator [J].
Alonso, JM ;
Ortega, R .
JOURNAL OF DIFFERENTIAL EQUATIONS, 1998, 143 (01) :201-220
[2]  
AMBROSETTI A., 1972, ANN MAT PUR APPL, V93, P231
[3]   CONTINUATION THEOREMS FOR PERIODIC PERTURBATIONS OF AUTONOMOUS SYSTEMS [J].
CAPIETTO, A ;
MAWHIN, J ;
ZANOLIN, F .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1992, 329 (01) :41-72
[4]  
CAPIETTO A, 1992, T AM MATH SOC, V329, P72
[5]  
Dancer E. N., 1976, Bulletin of the Australian Mathematical Society, V15, P321, DOI 10.1017/S0004972700022747
[6]  
DANCER EN, UNPUB PROOFS RESULTS
[7]   ON THE NUMBER OF 2-PI PERIODIC-SOLUTIONS FOR U'' + G(U) = S(1+H(T)) USING THE POINCARE-BIRKHOFF THEOREM [J].
DELPINO, MA ;
MANASEVICH, RF ;
MURUA, A .
JOURNAL OF DIFFERENTIAL EQUATIONS, 1992, 95 (02) :240-258
[8]  
DING W, 1983, P AM MATH SOC, V88, P41
[9]   LANDESMAN-LAZER CONDITIONS FOR PERIODIC BOUNDARY-VALUE-PROBLEMS WITH ASYMMETRIC NONLINEARITIES [J].
FABRY, C .
JOURNAL OF DIFFERENTIAL EQUATIONS, 1995, 116 (02) :405-418
[10]   Nonlinear resonance in asymmetric oscillators [J].
Fabry, C ;
Fonda, A .
JOURNAL OF DIFFERENTIAL EQUATIONS, 1998, 147 (01) :58-78