带积分边界条件的三阶微分方程迭代正解的存在性  

Existence and Iteration of Positive Solutions for Third-order Differential Equations with Integral Boundary Conditions

作　　者：郝彩云[1] 王文霞[1] 鞠梦兰 

机构地区：[1]太原师范学院数学系,山西晋中030619

出　　处：《河南大学学报（自然科学版）》2017年第3期372-378,共7页Journal of Henan University:Natural Science

基　　金：国家自然科学基金资助项目(11361047)

摘　　要：带有p-Laplace算子的微分方程边值问题在应用力学、天体物理等中有广泛的应用背景和非常重要的研究价值.本文通过将所研究问题转化为一个积分方程后,进而等价于算子的不动点问题,给出其Green函数的性质和算子的全连续性,应用单调迭代技术,获得了带p-Laplacian算子的三阶微分方程积分边值问题正解存在的充分条件,建立了迭代格式来逼近这个解,并且给出一个满足定理条件的例子.Boundary value problems of differential equations with p-Laplace operators have a wide range of applications and very important research value in the fields of applied mechanics, astrophysics, and so on. In this paper, through putting this problem into an integral equation, which is equivalent to the operator fixed point problem, and then combining its properties of Green function and the complete continuity of operator, by applying a monotone iteration technique, we obtain a sufficient condition for the existence of positive solution for third order differential equations with p-Laplacian, establish iterative schemes for approximating the solutions, and give a example which satisfies the condition of the theorem.

关 键 词：单调迭代方法 积分边界条件 正解 P—Laplacian算子 

分 类 号：O177.91[理学—数学]