四阶四点边值问题的上下解方法

The Method of Lower and Upper Solutions and the Existence of the Fourth-order Four-point Boundary Value Problem

应用单调迭代法建立了一类四阶四点边值问题｛u^(4)(t)=f(t,u(t)),0<t<1 u(0)=u(1)=0,au^n(ξ_1)-bu^m(ξ_1)=0,cu^n(ξ_2)+du^m(ξ_2)=0｝的上下解方法,这里a,b,c,d为非负数,0≤ξ_1<ξ_2≤1,满足ac(ξ_2-ξ_1)+ad+bc≠0.

In this paper we conceder the fourth-order four-point boundary value problem {u^（4）（t）=f（t,u（t））,0〈t〈1 u（0）=u（1）=0, au″（ξ1）-bu″′（ξ1）=0,cu″（ξ2）＋du″′（ξ2）=0 By dev61oping the upper and lower solution method and monotone iterative technique, we obtain some positive solutions, wherea, b, c, d are nonnegative,0≤ξ1〈ξ2≤1, and ac（ξ2-ξ1）＋ad＋bc≠0.