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一类二阶常微分方程无穷多点边值问题正解的存在性
引用本文:范虹霞.一类二阶常微分方程无穷多点边值问题正解的存在性[J].武汉大学学报(理学版),2011,57(1):88-92.
作者姓名:范虹霞
作者单位:兰州交通大学,数学系,甘肃,兰州,730070
基金项目:国家自然科学基金资助项目(10961017)
摘    要:运用锥上的不动点定理研究一类非线性二阶常微分方程无穷多点边值问题u″(t)+f(t,u)=0,t∈(0,1),u′(0)=∑∞αiu(ξi),u′(1)+∑∞βiu(ξi)=0,i=1i=1正解的存在性,其中αi,βi∈(0,+∞),i=1,2,…,n,…,0<ξ1<ξ2<…<ξn<…<1为给定的常数,f:0,1]×0,+∞)→0,+∞)连续.

关 键 词:无穷多点边值问题  正解    不动点

Existence of Positive Solutions for Second Order ∞-Point Boundary Value Problem
FAN Hongxia.Existence of Positive Solutions for Second Order ∞-Point Boundary Value Problem[J].JOurnal of Wuhan University:Natural Science Edition,2011,57(1):88-92.
Authors:FAN Hongxia
Institution:FAN Hongxia(Department of Mathematics,Lanzhou Jiaotong University,Lanzhou 730070,Gansu,China)
Abstract:In this paper,we investigate the existence of positive solutions to the following ∞-point boundary value problemu″(t)+f(t,u)=0,t∈(0,1), u′(0)=∑∞ i=1αiu(ξi),u′(1)+∑∞ i=1βiu(ξi)=0,where αi,βi are positive parameters,αi,βi∈(0,+∞),i=1,2,…,n,…,0<ξ1<ξ2<…<ξn<…<1,and f:×0,+∞)→0,+∞) is continuous.Based upon a fixed point theorem in cones,we show that the above problem has at least one positive solution if the nonlinearity f is either superlinear or sublinear.
Keywords:∞-point boundary value problem  positive solutions  cone  fixed point
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