This paper establishes criteria for the existence and non-existence of nonzero periodic solutions of the generalized Lienard equation （?）+f（x,（?））（?）+g（x）=0.The main goal is to study to what extent the dampi...This paper establishes criteria for the existence and non-existence of nonzero periodic solutions of the generalized Lienard equation （?）+f（x,（?））（?）+g（x）=0.The main goal is to study to what extent the damping f can be small so as to guarantee the existence of nonzero periodic solutions of such a system. With some standard edditional assumptions we prove that if for a small |x|, ∫<sup>±∞</sup>|f（x,y）|<sup>-1</sup>dy=±∞, then the system has at least one nonzero periodic solution, otherwise, the system has no nonzero periodic solution. Many classical and well-known results can be proved as corollaries to ours.展开更多
基金Supported by the National Natural Science Foundation of China.
文摘This paper establishes criteria for the existence and non-existence of nonzero periodic solutions of the generalized Lienard equation （?）+f（x,（?））（?）+g（x）=0.The main goal is to study to what extent the damping f can be small so as to guarantee the existence of nonzero periodic solutions of such a system. With some standard edditional assumptions we prove that if for a small |x|, ∫<sup>±∞</sup>|f（x,y）|<sup>-1</sup>dy=±∞, then the system has at least one nonzero periodic solution, otherwise, the system has no nonzero periodic solution. Many classical and well-known results can be proved as corollaries to ours.
