一类具混合边值条件的双参数奇摄动问题  

A Class of Two-Parameter Singularly Perturbed Problems with Mixed Boundary Value Conditions

作　　者：刘燕 LIU Yan(Department of Electronic Engineering, Wanjiang College of Anhui Normal University, Wuhu Anhui 241000, China)

机构地区：[1]安徽师范大学皖江学院电子工程系,安徽芜湖241000

出　　处：《西南师范大学学报（自然科学版）》2021年第7期26-38,共13页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：安徽省高校自然科学研究项目(KJ2020A1190).

摘　　要：考虑一类带非线性混合边值条件的四阶微分方程的双参数奇摄动问题,在适当的条件下,运用合成展开法,构造在两个小参数相互关联的3种不同情形下双参数奇摄动问题的形式渐近解,利用微分不等式理论证明了在3种情形下原问题解的存在性和渐近解的一致有效性.A class of singularly perturbed problems with two parameters for fourth-order differential equations with nonlinear mixed boundary value conditions have been discussed.Under appropriate conditions,the formal asymptotic solutions have been constructed under three different cases which the two small parameters are correlative using the composite expansion method.According to the theory of differential inequalities,the existence of solutions and the uniform validity of the asymptotic solutions in the three cases are proved.

关 键 词：奇摄动 非线性混合边值条件 双参数 微分不等式理论 

分 类 号：O175.14[理学—数学]