一类三阶三点非齐次边值问题的两个正解(英文)

Two positive solutions for third-order three-point nonhomogeneous boundary value problem

讨论三阶三点非齐次边值问题{u″′(t)+a(t)f(u(t))=0,0<t<1u(0)=u′(0)=0,u′(1)-αu′(η)=λ,其中η∈(0,1),α∈[0,1/η),λ∈(0,+∞).利用锥上的不动点定理,得到了上述边值问题两个正解存在的一些新结果.

The third-order three-point nonhomogeneous boundary value problemu″ ′ （t）＋a（t）f（u（t））=0,0t1u（0）=u′（0）=0,u′（1）-αu′（η）=λis considered in this paper,where η∈（0,1）,α∈[0,1/η） and λ∈（0,＋∞） are some parameters.By using Guo-Krasnosel＇skii fixed-point theorem,the new existence results of two positive solutions are obtained.