一类半线性奇摄动方程的无穷大边值问题  

Infinitely-Large Boundary Value Problems for a Class of Semi-Linear Singular Perturbed Equations

作　　者：杨雪洁[1] 陈雯[1] 孙国正[1] 

机构地区：[1]安徽师范大学数学计算机科学学院,安徽芜湖241000

出　　处：《安徽师范大学学报（自然科学版）》2014年第5期430-435,共6页Journal of Anhui Normal University(Natural Science)

摘　　要：本文主要研究了一类带非线性无穷大边界值条件的二阶半线性方程的奇摄动问题.在退化方程的解是(Ⅱn)(或(槇Ⅱn)或(Ⅲn)或(槇Ⅲn))稳定等条件下,利用界定函数法构造了问题的上、下解,并用微分不等式理论证明了该问题解的存在性,并给出了解的渐近估计.In this paper ,we study a class of singulary perturbed boundary value problems of second-order semi-linear equations with nonlinear and infinitely-large boundary value conditions . Under the condition that the reduced solution is （ Ⅱ n ）（or （ Ⅱ n ） or （ Ⅲ n ） or （ Ⅲ n ）） stable ,we construct the upper and lower solutions by making use of the method of bounding functions . Then the existence of the solutions are proved and the asymptotic estimate of solutions are given by the theory of differential inequality .

关 键 词：奇摄动 无穷大边界值 非线性边界条件 微分不等式理论 

分 类 号：O175.14[理学—数学]