一类含参数非线性三阶两点边值问题正解的存在性  

Existence of positive solutions for a class of nonlinear third-order two-point boundary value with parameter

作　　者：武晨[1] WU Chen(Branch of Nanjing,JiangSu Union Technical Institute,Nanjing Jiangsu 210019,China)

机构地区：[1]江苏联合职业技术学院南京分院,江苏南京210019

出　　处：《阜阳师范学院学报（自然科学版）》2018年第3期8-10,共3页Journal of Fuyang Normal University(Natural Science)

基　　金：江苏省教育科学"十三五"规划课题(B-b/2016/03/55);江苏省职业教育教学改革研究课题(ZZZ5)资助

摘　　要：本文借助于锥上的不动点定理,考虑如下一类非线性三阶两点点边值问题:{u?(t)+λa(t)f(u(t))=0,t∈(0,1),u(0)=u′(0)=u″(1)=0,解的存在性,其中λ>0,f:[0,+∞)→[0,+∞),连续a:(0,1)→[0,+∞),连续且满足0<∫_1~0(t-(1/2)(t^2))a(t)dt<+∞,允许a(t)在t=0或者t=1处奇异。In this paper,we study the existence of positive solution to the following third-order two-point boundary value problems:ì{u'''(t)+λa(t)f(u(t))=0,t∈(0,1),u(0)=u′(0)=u″(1)=0,whereλis a positive parameter,f:[0,+∞)→[0,+∞)a:(0,1)→[0,+∞)are continuous,0<∫0 1(t-12 t2)a(t)dt<+∞and a(t)may be singular at t=0 or t=1,the proof of the main results is based on the fixed-point on cone.

关 键 词：三阶两点边值问题 锥 正解 格林函数 

分 类 号：O175.8[理学—数学]