中文摘要：

该文考虑了下面的具一维p-Laplacian算子的多点边值问题其中φ_p（s）=｜s｜~（p-2）s,p〉1,α_i〉0,β_i〉0,0〈sum from i=1 to m-1α_iξ_i≤1,0〈sum from i=1 to m-1β_i（1-η_i）≤1,0=ξ_0〈ξ_1〈ξ_2〈…〈ξ_（m-1）〈η_1〈η_2〈…〈η_（m-1）〈η_m=1,i=1,2,…,m-1.通过运用锥上的不动点定理,该文得到了至少三个正解的存在性.有趣的是文中的边界条件是一个新型的Sturm-Liouville型边界条件,这类边值问题到目前为止还很少被研究.

英文摘要：

In this paper,we are concerned with the following multi-point boundary valueproblem with one-dimensional p-Laplacian■whereφ_p（s） = ｜s｜~（p-2）s,p1,α_i0,β_i0,0■α_iξ_i≤1,0■β_i（1 -η_i）1,0 =ξ_0oξ_1ξ_2…ξ_（m-1）η_1η_2…η_（m-1）η_m = 1,i = 1,2,…,m - 1.By using afixed point theorem in a cone,we obtain the existence of three positive solutions at least.Theinteresting point is that the boundary condition is a new kind of Sturm-Liouville type boundarycondition,which has rarely been treated up to now.