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Applied Mathematics and Mechanics (English Edition) ›› 2001, Vol. 22 ›› Issue (3): 282-293.

• 论文 • 上一篇    下一篇

ON THE ASYMPTOTIC SOLUTIONS OF BOUNDARY VALUE PROBLEMS FOR A CLASS OF SYSTEMS OF NONLINEAR DIFFERENTIAL EQUATIONS (Ⅰ)

江福汝   

  1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P. R. China
  • 收稿日期:2000-03-21 修回日期:2000-09-23 出版日期:2001-03-18 发布日期:2001-03-18

ON THE ASYMPTOTIC SOLUTIONS OF BOUNDARY VALUE PROBLEMS FOR A CLASS OF SYSTEMS OF NONLINEAR DIFFERENTIAL EQUATIONS (Ⅰ)

JIANG Fu-ru   

  1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P. R. China
  • Received:2000-03-21 Revised:2000-09-23 Online:2001-03-18 Published:2001-03-18

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摘要： A new method is applied to study the asymptotic behavior of solutions of boundary value problems for a class of systems of nonlinear differential equations u″=v, εv″+ f(x,u,u′)v′-g(x,u,u′)v=0 (0<ε<<1). The asymptotic expansions of solutions are constructed, the remainders are estimated. The former works are improved and generalized.

关键词: system of nonlinear differential equations, boundary value problems, asymptotic solution

Abstract: A new method is applied to study the asymptotic behavior of solutions of boundary value problems for a class of systems of nonlinear differential equations u″=v, εv″+ f(x,u,u′)v′-g(x,u,u′)v=0 (0<ε<<1). The asymptotic expansions of solutions are constructed, the remainders are estimated. The former works are improved and generalized.

Key words: system of nonlinear differential equations, boundary value problems, asymptotic solution

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