三阶两点边值问题正解的存在性  

Existence of positive solution for a third-order twopointboundary value problems

作　　者：庄国华[1] 

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）》2017年第4期12-14,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)资助

摘　　要：本文研究一类非线性三阶两点点边值问题:{u?(t)+a(t)f(u(t))=0,t?(0,1)u(0)=u′(0)=u″(1)=0,正解的存在性,其中f:[0,+∞)→[0,+∞)连续,a:(0,1)→[0,+∞)连续且满足0<∫01(t-1/2t^2)a(t)dt<+∞,允许a(t)在t=0或者t=1处奇异。通过利用锥上的不动点的定理得到上述边值问题正解的存在性结果。This paper studied the existence of positive solution to the following third-order two-point boundary value problems:{u?(t)+a(t)f(u(t))=0,t?(0,1)u(0)=u′(0)=u″(1)=0,where f:[0,+∞)→[0,+∞), a:(0,1)→[0, +∞) are continuous,0<∫01(t-1/2t^2)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：锥 格林函数 正解 边值问题 

分 类 号：O175.8[理学—数学]