三阶三点非齐次边值问题多个正解的存在性

Existence of Multiple Positive Solutions of Third-Order Three-Point Non-homogeneous Boundary Value Problems

通过利用锥上的不动点定理讨论了下列三阶三点边值问题u(t)+a(t)f(t,u(t))=0,0<t<1u(0)=u′(0)=0,u′(1)-αu′(η)=λ,多个正解的存在性,这里η∈(0,1),α∈[0,η1)是常数,λ∈(0,+∞)是一个参数.

We employed the fixed-point theorem of cone expansion and compression to discuss the existence of multiple positive solutions of the following third-order three-point boundary value problems {u″′（t）＋a（t）f（t,u（t））=0,0〈t〈1 u（0）=u＇（0）=0,u＇（1）-au＇（η）=λ,where η∈（0,1）,α∈[0,1/η）are constants and λ∈（0,＋∞）is a parameter.