奇异三阶广义右聚焦边值问题的正解  

POSITIVE SOLUTIONS OF SINGULAR THIRD-ORDER GENERALIZED RIGHT FOCAL BOUNDARY VALUE PROBLEMS

作　　者：姚庆六[1] 

机构地区：[1]南京财经大学应用数学系,南京210003

出　　处：《系统科学与数学》2013年第4期480-487,共8页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(11071109)资助课题

摘　　要：考察了非线性三阶三点广义右聚焦边值问题u′″(t)=f(t,u(t)),0<t<1,u(0)=u′(η)=0,γu(1)+δu″(1)=0的正解存在性与多解性,其中1/2<η<1并且f(t,u)可以在t=0,t=1及u=0处奇异.通过引入两个非线性项在燕尾形区域上的高度函数,并且考察这些高度函数的积分来估计解的先验界.根据锥拉伸锥压缩型的Guo-Krasnoselskii不动点定理获得了某些新的结论.The existence and multiplicity of positive solutions are considered for the nonlinear third-order three-point generalized right focal boundary value problems where 1/2 〈 η 〈 1 and the nonlinear term f（t, u） may be singular at t=0, t = 1 and u = O. By introducing two height functions of the nonlinear term on some swallow- tailed regions and considering integrations of the height functions, the a priori bound of solution is estimated. According to the Guo-Krasnoselskii fixed point theorem of cone expansion-compression type, several new results are obtained.

关 键 词：奇异常微分方程 多点边值问题 正解 存在性 多解性 

分 类 号：O175.8[理学—数学]