In this paper, by using of the theory of coincidence degree ,we obtain the new conditions which guarantee the existence of harmonic solutions for Lienard Systems our resuls do not require that the damping must be pos...In this paper, by using of the theory of coincidence degree ,we obtain the new conditions which guarantee the existence of harmonic solutions for Lienard Systems our resuls do not require that the damping must be positire.展开更多
In the paper we generalize some classic results on limit cycles of Liénard system x=φ(y)-F(x),y=-g(x)having a unique equilibrium to that of the system with several equilibria.As applications,we strictly prove th...In the paper we generalize some classic results on limit cycles of Liénard system x=φ(y)-F(x),y=-g(x)having a unique equilibrium to that of the system with several equilibria.As applications,we strictly prove the number of limit cycles and obtain the distribution of limit cycles for three classes of Liénard systems,in which we correct a mistake in the literature.展开更多
文摘In this paper, by using of the theory of coincidence degree ,we obtain the new conditions which guarantee the existence of harmonic solutions for Lienard Systems our resuls do not require that the damping must be positire.
基金supported by the National Key R&D Program of China(Grant No.2022YFA1005900)Chen is supported by the National Natural Science Foundation of China(Grant Nos.12322109,12171485)+3 种基金Science and Technology Innovation Program of Hunan Province(Grant No.2023RC3040)supported by the National Natural Science Foundation of China(Grant No.12271355)supported by the National Natural Science Foundation of China(Grant No.12271353)the Innovation Program of Shanghai Municipal Education Commission(Grant No.2021-01-07-00-02-E00087)。
文摘In the paper we generalize some classic results on limit cycles of Liénard system x=φ(y)-F(x),y=-g(x)having a unique equilibrium to that of the system with several equilibria.As applications,we strictly prove the number of limit cycles and obtain the distribution of limit cycles for three classes of Liénard systems,in which we correct a mistake in the literature.
