Singular perturbation of a second-order three-point boundary value problem for nonlinear systems  

作　　者：林晓洁 刘文斌 

机构地区：[1]Department of Mathematics,China University of Mining and Technology [2]School of Mathematical Science,Xuzhou Normal University

出　　处：《Journal of Shanghai University(English Edition)》2009年第1期16-19,共4页上海大学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant No.10771212);the Natural Science Foundation of Jiangsu Province (Grant No.BK2008119);the Natural Science Foundation of the Education Division of Jiangsu Province (Grant No.08KJB110011)

摘　　要：This paper deals with the existence of solutions to a singularly perturbed second-order three-point boundary value problem for nonlinear differential systems. The authors construct an appropriate generalized lower- and upper-solution pair, a concept defined in this paper, and employ the Nagumo conditions and algebraic boundary layer functions to ensure the existence of solutions of the problem. The uniformly valid asymptotic estimate of the solutions is given as well. The differential systems have nonlinear dependence on all order derivatives of the unknown.This paper deals with the existence of solutions to a singularly perturbed second-order three-point boundary value problem for nonlinear differential systems. The authors construct an appropriate generalized lower- and upper-solution pair, a concept defined in this paper, and employ the Nagumo conditions and algebraic boundary layer functions to ensure the existence of solutions of the problem. The uniformly valid asymptotic estimate of the solutions is given as well. The differential systems have nonlinear dependence on all order derivatives of the unknown.

关 键 词：singular perturbation nonlinear systems three-point boundary value problem upper and lower solutions 

分 类 号：O175.8[理学—数学]