EXISTENCE OF BOUNDED SOLUTIONS ON THE REAL LINE FOR LIÉNARD SYSTEM

Applied Mathematics and Mechanics (English Edition) ›› 2003, Vol. 24 ›› Issue (4): 479-490.

EXISTENCE OF BOUNDED SOLUTIONS ON THE REAL LINE FOR LIÉNARD SYSTEM

肖海滨

Department of Mathematics, Faculty of Sciences, Ningbo University, Ningbo, Zhejiang 315211, P. R. China

收稿日期:2002-01-21 修回日期:2003-01-17 出版日期:2003-04-18 发布日期:2003-04-18

EXISTENCE OF BOUNDED SOLUTIONS ON THE REAL LINE FOR LIÉNARD SYSTEM

XIAO Hai-bin

Department of Mathematics, Faculty of Sciences, Ningbo University, Ningbo, Zhejiang 315211, P. R. China

Received:2002-01-21 Revised:2003-01-17 Online:2003-04-18 Published:2003-04-18

摘要/Abstract

摘要： The existence of monotone and non-monotone solutions of boundary value problem on the real line for Li閚ard equation is studied. Applying the theory of planar dynamical systems and the comparison method of vector fields defined by Li閚ard system and the system given by symmetric transformation or quasi-symmetric transformation, the invariant regions of the system are constructed. The existence of connecting orbits can be proved. A lot of sufficient conditions to guarantee the existence of solutions of the boundary value problem are obtained. Especially, when the source function is bi-stable, the existence of infinitely many monotone solusion is obtained.

Abstract: The existence of monotone and non-monotone solutions of boundary value problem on the real line for Liénard equation is studied. Applying the theory of planar dynamical systems and the comparison method of vector fields defined by Liénard system and the system given by symmetric transformation or quasi-symmetric transformation, the invariant regions of the system are constructed. The existence of connecting orbits can be proved. A lot of sufficient conditions to guarantee the existence of solutions of the boundary value problem are obtained. Especially, when the source function is bi-stable, the existence of infinitely many monotone solusion is obtained.

中图分类号:

O175
35K57

肖海滨. EXISTENCE OF BOUNDED SOLUTIONS ON THE REAL LINE FOR LIÉNARD SYSTEM[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(4): 479-490.

XIAO Hai-bin . EXISTENCE OF BOUNDED SOLUTIONS ON THE REAL LINE FOR LIÉNARD SYSTEM[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(4): 479-490.

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EXISTENCE OF BOUNDED SOLUTIONS ON THE REAL LINE FOR LIÉNARD SYSTEM

EXISTENCE OF BOUNDED SOLUTIONS ON THE REAL LINE FOR LIÉNARD SYSTEM

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