一类含一阶导数的二阶m点边值问题多解的存在性

Multiplicity Results for Second-order m-point Boundary Value Problem With First Derivative

通过利用Avery-Peterson不动点定理讨论了一类二阶m点边值问题x″+f(t,x,x′)=0,x(0)=∑m-2i=1αix(ξi),x′(1)=∑m-2i=1βix′(ξi),正解的存在性,在适当条件下建立了这类边值问题至少存在三个的正解的充分条件.

By using Avery-Peterson fixed point theorem,we discuss second-order m-point boundary value problem,x″＋f（t,x,x′）=0,x（0）=∑m-2[]i=1αix（ξi）,x′（1）=∑m-2[]i=1βix′（ξi）.Under appropriate assumptions,sufficient conditions for the existence of at least three positive solutions are established.