关键词: 无穷多点边值问题, 正解, 锥, 不动点

Abstract:

Let α _i ∈[0,  ∞), ξ _i ∈ (0,1) and ∑^∞_i=1α _i ξ _i <1.  We study the existence of positive solutions to  the  boundary value problem

u''+a(t) f(u)=0,  t  ∈(0, 1),
u(0)=0,  u(1)= ∑^∞_{i =1} α _i u ( ξ _i ) ,
where α ∈ C([0, 1], [0, ∞)), and f:[0, ∞) → [0, ∞) is continuous. We show the existence of at least one positive solution if f is either superlinear or sublinear by applying a fixed-point theorem in cones.

Key words: ∞-point boundary value problem, Positive solution, Cone, Fixed point