Some sharp sufficient conditions for generalized Lienard systems to have positive or negative semi-orbits which do not cross the vertical isocline are given. Applications of the main results to some polynomial systems...Some sharp sufficient conditions for generalized Lienard systems to have positive or negative semi-orbits which do not cross the vertical isocline are given. Applications of the main results to some polynomial systems are also presented.展开更多
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
The main purpose of this paper is to obtain some new sufficient conditions for the continuability of solutions in the future of the lienard system: X'=y-F(x), y'=-g(x).
In the present paper the concepts “the critical point system” and “the critical point-cycle system” with index +1 are introduced for the system of the form where (y) and g(x) may have several zero points.Then we s...In the present paper the concepts “the critical point system” and “the critical point-cycle system” with index +1 are introduced for the system of the form where (y) and g(x) may have several zero points.Then we show that Dragilev's Theorem,Zhang Zhi-fen's Theorem etc.,after appropriate mo- dification can be used to discuss the existence and uniqueness of limit cy- cles aroud several critical points.Finally,making use of these results,we give more complete qualitative analysis for a self-excited system with th- ree equilibrium positions,governed by-the equation展开更多
In this paper,some known results concerning the nonexistence of non-trivial periodic solutions for the Lienard system are extended to the more general system
This paper discusses the local and global center of the generalized Lienard system, gives two theorems which extend and improve the relative results of [1]-[3]. Moreover the lemmas in this paper are also useful to the...This paper discusses the local and global center of the generalized Lienard system, gives two theorems which extend and improve the relative results of [1]-[3]. Moreover the lemmas in this paper are also useful to the study for the oscillation, stability and the existence of limit cycles of the generalized Lienard system.展开更多
This paper gives a theorem for the local center of generalized Lienard system; the relative theorems in the references can be deduced from our corollaries.
通过构造辅助方程,求出了具五次强非线性项的L ienard方程的多种新精确解,包括孤波解、三角函数解、Jacob i椭圆函数解.利用所得结果可以求出Kundu方程、导数Schr d inger方程和力学中重要的具五次强非线性项的波方程以及PC方程等重要...通过构造辅助方程,求出了具五次强非线性项的L ienard方程的多种新精确解,包括孤波解、三角函数解、Jacob i椭圆函数解.利用所得结果可以求出Kundu方程、导数Schr d inger方程和力学中重要的具五次强非线性项的波方程以及PC方程等重要非线性发展方程的精确解.展开更多
文摘Some sharp sufficient conditions for generalized Lienard systems to have positive or negative semi-orbits which do not cross the vertical isocline are given. Applications of the main results to some polynomial systems are also presented.
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.
文摘The main purpose of this paper is to obtain some new sufficient conditions for the continuability of solutions in the future of the lienard system: X'=y-F(x), y'=-g(x).
文摘In the present paper the concepts “the critical point system” and “the critical point-cycle system” with index +1 are introduced for the system of the form where (y) and g(x) may have several zero points.Then we show that Dragilev's Theorem,Zhang Zhi-fen's Theorem etc.,after appropriate mo- dification can be used to discuss the existence and uniqueness of limit cy- cles aroud several critical points.Finally,making use of these results,we give more complete qualitative analysis for a self-excited system with th- ree equilibrium positions,governed by-the equation
文摘In this paper, the uniqueness of limit cycle of a special polynomial Lienard system is discussed and some results under certain conditions are given.
文摘In this paper,some known results concerning the nonexistence of non-trivial periodic solutions for the Lienard system are extended to the more general system
文摘This paper discusses the local and global center of the generalized Lienard system, gives two theorems which extend and improve the relative results of [1]-[3]. Moreover the lemmas in this paper are also useful to the study for the oscillation, stability and the existence of limit cycles of the generalized Lienard system.
文摘This paper gives a theorem for the local center of generalized Lienard system; the relative theorems in the references can be deduced from our corollaries.
