Acta mathematica scientia,Series B ›› 1998, Vol. 18 ›› Issue (1): 113-120.

• Articles • Previous Articles    

BOUNDEDNESS OF SOLUTIONS AND EXISTENCE OF LIMIT CYCLES FOR A NONLINEAR SYSTEM OF DIFFERENTIAL EQUATIONS

Huang Lihong1, Chen Mingpo2   

  1. 1. Department of Applied Mathematics, Hanan University, Changsha 410082, China;
    2. Institute of Mathematics, Academia Sinica, Nankang, Taipei, 11529 Taiwan, China
  • Received:1966-03-25 Online:1998-03-25 Published:1998-03-25
  • Supported by:
    This work was supported by the NNSF of China

Abstract: In this paper, author obtain sufficient conditions for the boundedness of solutions and the existence of limit cycles of the nonlinear differential system
dx/dt=p(y),dy/dt=-q(y)h(x,y)-g(x) without the traditional assumptions "h(x, y) ≥ 0 for|x|sufficiently large" and "∫0±∞ g (x)dx=+∞".

Key words: Nonlinear differential system, boundedness, existence, limit cycle

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