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Applied Mathematics and Mechanics (English Edition) ›› 1984, Vol. 5 ›› Issue (5): 1659-1665.

• Articles • 上一篇    下一篇

PERTURBATION SOLUTION OF THE WEAK-NONLINEAR DIFFERENTIAL EQUATION WITH δ-FUNCTION

刘曾荣, 魏锡荣   

  1. Anhui University, Heifei
  • 收稿日期:1983-01-14 出版日期:1984-09-18 发布日期:1984-09-18

PERTURBATION SOLUTION OF THE WEAK-NONLINEAR DIFFERENTIAL EQUATION WITH δ-FUNCTION

Liu Zheng-rong, Wei Si-rong   

  1. Anhui University, Heifei
  • Received:1983-01-14 Online:1984-09-18 Published:1984-09-18

摘要： In this paper,starting from some fundamental properties of Heaviside function and δ -function,making use of singular perturbation methods we provide a method of finding the asymptotic analytic solution of equationwhere M(u)=eƒ+λ#948;(t-a) is an n -order linear differential operator,ƒ(u) is a polynomial. By means of this method,we discuss some examples concretely. The results can be explained satisfactorily in physics. If we deal with linear problem by this method,the result will agree with that drawn from theorem of impulse.

关键词: bilevel generalized mixed equilibrium problem (BGMEP), generalized mixed variational-like inequality problem (GMVLIP), auxiliary principle, iterative algorithm, reflexive Banach space

Abstract: In this paper,starting from some fundamental properties of Heaviside function and δ -function,making use of singular perturbation methods we provide a method of finding the asymptotic analytic solution of equationwhere M(u)=eƒ+λ#948;(t-a) is an n -order linear differential operator,ƒ(u) is a polynomial. By means of this method,we discuss some examples concretely. The results can be explained satisfactorily in physics. If we deal with linear problem by this method,the result will agree with that drawn from theorem of impulse.

Key words: bilevel generalized mixed equilibrium problem (BGMEP), generalized mixed variational-like inequality problem (GMVLIP), auxiliary principle, iterative algorithm, reflexive Banach space

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