XIAO Hai-bin. Existence of Bounded Solutions on the Real line for Lienard System[J]. Applied Mathematics and Mechanics, 2003, 24(4): 423-433.
Citation:
XIAO Hai-bin. Existence of Bounded Solutions on the Real line for Lienard System[J]. Applied Mathematics and Mechanics, 2003, 24(4): 423-433.
XIAO Hai-bin. Existence of Bounded Solutions on the Real line for Lienard System[J]. Applied Mathematics and Mechanics, 2003, 24(4): 423-433.
Citation:
XIAO Hai-bin. Existence of Bounded Solutions on the Real line for Lienard System[J]. Applied Mathematics and Mechanics, 2003, 24(4): 423-433.
Existence of Bounded Solutions on the Real line for Lienard System
Department of Mathematics, Faculty of Sciences, Ningbo University, Ningbo, Zhejiang 315211, P. R. China
Received Date: 2002-01-21Rev Recd Date:
2003-01-17
Publish Date:
2003-04-15
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,dymamical 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.Espeaaly,when the source function is bi-stable,tiie existence of infinitely many monotone solusion is obteained.
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