一类二阶常微分方程无穷多点边值问题正解的存在性

一类二阶常微分方程无穷多点边值问题正解的存在性 Existence of Positive Solutions for Second Order ∞-Point Boundary Value Problem 范虹霞 FAN Hongxia 1 first-author 兰州交通大学数学系 兰州交通大学数学系 Department of Mathematics,Lanzhou Jiaotong University Department of Mathematics,Lanzhou Jiaotong University 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. 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. 无穷多点边值问题 正解 锥 不动点 ∞-point boundary value problem positive solutions cone fixed point 10.14188/j.1671-8836.2011.01.001 O175.8 国家自然科学基金资助项目（10961017） 2011-01-01 2021-04-01 1 57