本文用锥上的Krasnoselskii's不动点定理研究了具有p-Laplace算子的三点边值问题: {((ψ)p(u'(t)))'+a(t)f(u(t))=0,t∈(0,1), u(0)=αu(η),u(1)=βu(η), 其中0<α,β<1,0<η<1且(ψ)p(z)=|z|^p-2z,p>1.在f满足一定的增长条件下,得到方程正解的存在性.作为应用,给出两个例子.
By means of the Krasnoselskii's fixed-point theorem in cone, we study the existence of positive solution for the three-point boundary value problem with p-Laplacian operator {((ψ)p(u'(t)))'+a(t)f(u(t))=0,t∈(0,1), u(0)=αu(η),u(1)=βu(η), where0〈α,β〈1,0〈η〈1 and (ψ)p(z)=|z|^p-2z,p〉1.Sufficient conditions are given whichguarantee the existence of positive solutions of this problem.