带变号系数的非线性二阶两点边值问题的正解

摘要

研究了非线性两点边值问题u"(t)+h(t)f(u(t))＝0,0≤t≤1, u(0)＝u(1)＝0的一、二及三个正解的存在性,其中,f≥0并且允许h在[0,1]上改变符号,主要工具是锥压缩与锥拉伸型的Krasnosel'skii不动点定理.%The existence of one,two and three positive solutions to the nonlinear two-point boundary value problem u"(t)+h(t)f(u(t))=0, u(0)=u(1)=0 is studied,where f≥0 and coefficient h is allowed to change sign on [0,1].Main tool is Krasnosel'skii fixed point theorem of cone expansion-compression type.