一类非线性四阶三点边值问题的正解存在性与多解性

The existence and multiplicity of positive solutions for a nonlinear fourth-order three-point boundary value problems

考虑非线性四阶三点边值问题(P)u(4)(t)=h(t)f(u),0<t<1,u(0)=u′(1)=u″(0)=u″(η)-u″(1)=0.通过利用锥上的Krasnosel′skii不动点定理,不仅获得了边值问题(P)的至少一个正解的存在性结果,而且建立了问题(P)的无穷多个正解的存在性定理.

A nonlinear fourth-order three-point boundary value problem （P）{u（4）（t）=h（t）f（u）,0t1,u（0）=u′（1）=u″（0）=u″（η）-u″（1）=0 is considered.By using Krasnosel′skii fixed point theorem in cones,results on existence of at least one positive solution to the boundary value problem（P） are obtained,and existence theorem of infinitely many positive solution to the problem（P） is established.