摘要
应用不动点指数理论,在与相应线性算子本征值有关的条件下,得到了高阶(k, n-k)多点边值问题(-1)n-kφ(n)(x)=h(x)f(φ(x)),0<x<1,n≥2,1≤k≤n-1 分别在边值条件正解的存在性结果,其中0<ξ1<ξ2<…<ξm-2<1,ai∈[0,∞),并且允许h(x) 在x=0和x=1奇异.
By means of the fixed point index under some conditions concerning the eigenvalues corresponding to the relevant linear operator, the existence is obtained in this paper for the multi point boundary value problem of the higher order (k, n - k) differential equation (-1)^n-kφ(n)(x)=h(x)f(φ(x)),0〈x〈1,n≥2,1≤k≤n-1, subject to the boundary value conditions
φ(0)=∑i-1^m-2aiφ(ξi),φ^(i)(0)=φ^(j)(1)=0,1≤i≤k-1,0≤j≤n-k-1,
φ(1)=∑i-1^m-2aiφ(ξi),φ^(i)(0)=φ^(j)(1)=0,1≤i≤k-1,0≤j≤n-k-1
respectively, where 0〈ξ1〈ξ2〈…〈ξm-2〈1,ai∈[0,∞), and h(x) is allowed to be singular at x = 0 and x = 1.
出处
《数学学报(中文版)》
SCIE
CSCD
北大核心
2006年第2期391-398,共8页
Acta Mathematica Sinica:Chinese Series
基金
国家自然科学基金资助项目(10371066
10371013)
关键词
边值问题
正解
锥
boundary value problem
positive solution
cone