带积分边界条件的三阶微分方程凸单调正解的存在唯一性  

Existence and Uniqueness of Convex Monotone Positive Solutions for Third-Order Boundary Value Problems 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：《烟台大学学报（自然科学与工程版）》2017年第1期11-16,共6页Journal of Yantai University(Natural Science and Engineering Edition)

基　　金：国家自然科学基金资助项目(11361407)

摘　　要：研究了带积分边界条件的三阶边值问题凸单调正解的存在唯一性,证明利用了和算子的不动点定理以及混合单调算子中的不动点定理,获得了所研究问题凸单调正解存在唯一的充分条件,并且建立了迭代格式来逼近这个唯一正解.We investigate the existence and uniqueness of convex monotone positive solutions for third-order bound- ary value problems with integral boundary conditions. By means of a fixed point therorem of sum operator and a fixed point theorem of mixed monotone operator, we obtain some sufficient conditions for the existence of positive solutions for the problem, and establish iterative schemes for approximating the solution.

关 键 词：正解 积分边值问题 不动点 和算子 混合单调算子 

分 类 号：O177.91[理学—数学]