半正(p,n-p)右聚焦边值问题的正解

Positive solutions for semipositone (p,n-p) right focal boundary value problems

研究了半正(p,n-p)(1 p n-1)右聚焦边值问题(-1)n-pun=fλ(t,u),t∈(0,1)u(i)(0)=0,0 i p-1,正解的存在性,利用Guo-Krasnoselskii不动点定理,获得并证明了正解的存在性定理.这里f(t,u)-M,M为正常数.

In this paper, we study the existence of positive solutions of the （ p, n-p） （1≤p≤n - 1 ） right focal boundary value problem {（-1）^n-pu^n=λf（t,u）,t∈（0,1）u^（i）（0）=0,0≤i≤p-1,u^（i）（0）=0,p≤i≤n-1,where f（ t, u ）≥- M, M is a positive constant. Meanwhile, the existence of positive solutions by means of a fixed theorem of Guo-Krasnoselskii.