三阶奇摄动非线性边值问题  

Third Order Nonlinear Singularly Perturbed Boundary Value Problem

作　　者：王国灿[1] 金丽[1] 

机构地区：[1]大连铁道学院文理分院,大连116028

出　　处：《应用数学和力学》2002年第6期597-603,共7页Applied Mathematics and Mechanics

摘　　要：利用微分不等式理论 ,研究了某一类三阶奇摄动非线性边值问题·　以二阶边值问题的已知结果为基础 ,引入Volterra型积分算子 ,建立了三阶非线性边值问题的上下解方法·　在适当条件下 ,构造出具体的上下解 。Third order singulary perturbed boundary value problem by means of differential inequality theories is studied. Based on the given results of second order nonlinear boundary value problem, the upper and lower solutions method of third order nonlinear boundary value problems by making use of volterra type integral operator was established. Specific upper and lower solutions were constructed, and existence and asymptotic estimates of solutions under suitable conditions were obtained. The result shows that it seems to be new to apply these techniques to solving these kinds of third order singularly perturbed boundary value problem. An example is given to demonstrate the applications.

关 键 词：三阶非线性边值问题 上下解 Volterra型积分算子 存在性 渐近估计 

分 类 号：O175.8[理学—数学]