一类非线性变号二阶边值问题正解的存在性

The Existence of Positive Solutions to Nonlinear Second Order Boundary Value Problem with Change of Sign

考虑一类非线性变号二阶三点边值问题u+h(t)f(u(t))=0,t∈[0,1],u(0)=au'(0),u(1)=βu(n),其中α≥0,0<β<1,n∈(0,1),h(t)≥0,t∈[0,n],h(t)≤0,t∈[n,1],运用锥上的Guo-Krasnoselskii’s不动点定理研究一类非线性变号二阶三点边值问题至少存在两个正解u1,u2,且0<‖u1‖<‖u2‖.

This paper studies the following nonlinear second order three-point boundary value problem u＋h（t）f（u（t））=0,t∈[0,1],u（0）=au＇（0）,u（1）=βu（n）,where α≥0,0〈β〈1,n∈（0,1）,h（t）≥0,t∈[0,n],h（t）≤0,t∈[n,1],The existence of at least two positive solutions is studied by using the Guo-Krasnoselskii＇s fixed-point theorem in cones.