一类二阶半正问题正解的存在性

Existence of positive solutions for a class of second order semipositone problems

研究二阶半正问题{-u"(t)=λh(t)f(u(t)),t∈(0,1),αμ(0)-b(μ'(0))μ'(0)=0,c(μ(1))μ(1)+8μ'(1)=0正解的存在性,其中λ为正参数,α,δ>0为常数,b,c∈C([0,∞),[0,∞)),h∈C([0,1],[0,∈)),f∈C([0,∞),R),f>-M(M>0)且f∞:=lim_(x→∞)f(x)/x=∞。主要定理的证明基于Krasnoselskii不动点定理。

The existence of positive solutions for the second order semipositone problem{-u"(t)=λh(t)f(u(t)),t∈(0,1),αμ(0)-b(μ'(0))μ'(0)=0,c(μ(1))μ(1)+8μ'(1)=0 is studied,where^is a positive parameter,α,δ>0 are constants b,c∈C([0,∞),[0,∞)),h∈C([0,1],[0,∈)),f∈C([0,∞),R),f>-M(M>0)and f∞:=lim_(x→∞)f(x)/x=∞.The proof of the main theorems is based on fixed point theorem of Krasnoselskii.