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

  • Received Date: 2002-01-21
  • Rev Recd Date: 2003-01-17
  • Publish Date: 2003-04-15
  • 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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  • [1]
    Aizik V,Vitaly V,Vladimir V.Travelling Wave Solution of Parabolic System[M].New York:Springer-Verlag,1994,31-32.
    [2]
    Chicone C.Ordinary Differential Equation With Application[M].New York:Springer-Verlag,1999,274-278.
    [3]
    Snchez-GarduAno F,Maini P K.Travelling wave phenomena in some degenerate reaction diffusion equation[J].J Differential Equations,1995,117:281-319.
    [4]
    Aronson D G,Weiberger H F.Multidimentional nonlinear diffusion arising in population genetics[J].Advance in Mathematics,1978,33:33-76.
    [5]
    Gilbarg D.The existence and limit behavior of the one-dimensional shock layer[J].Amer J Math,1951,7:256-274.
    [6]
    Malagati L,Marcelli C.Existence of bounded trajectories via upper and low solution[J].Discrete and Continuous Dynamical System,2000,6(3):575-590.
    [7]
    Gordon P.Pathes connecting elementary critical points of dynamical system[J].SIAM J Appl Math,1974,26(1):35-102.
    [8]
    АвдонинНИ.Овзаиморасположениилиниираэдела[J].ДиффУрав,1968,4(12):2231-2242.
    [9]
    АвдонинНИ.Некоторыепрпзнакисуществованияиотсутсутствиязамкинутыхтраекторийоднойсистемыдифференциальныхуравнений[J].ДиффУрав,1968,4(4):639-645.
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