CAJ | 학술논문

万方数据

曲阜师范大学学报（自然科学版） 곡부사범대학학보（자연과학판）
JOURNAL OF QUFU NORMAL UNIVERSITY (NATURAL SCIENCE EDITION)
2010年 4期 21-28 ,共8页

栾世霞%张忠华欒世霞%張忠華

란세하%장충화

非线性三点边界条件%不动点定理%奇异%锥非線性三點邊界條件%不動點定理%奇異%錐
비선성삼점변계조건%불동점정리%기이%추
Nonlinear three-point boundary condition%fixed point theorem%singularity%cone

利用锥上的不动点定理给出了下述非线性三点边值问题:(φ(u'))'+a(t)f(u)=0, 0＜t＜1正解和可数多个正解的存在性的一个结果. 这里φ是R→R的增的同胚和同态映射,φ(0)=0.
이용추상적불동점정리급출료하술비선성삼점변치문제:(φ(u'))'+a(t)f(u)=0, 0＜t＜1정해화가수다개정해적존재성적일개결과. 저리φ시R→R적증적동배화동태영사,φ(0)=0.
In this paper, we consider three-point nonlinear boundary value problem for the equation(φ(u'))'+a(t)f(u)=0, 0＜t＜1,where φ:R→R is an increasing homeomorphism and homomorphism with φ(0)=0. We show the existence of positive solutions and countably many positive solutions by fixed point theorems in a cone.