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Let α,β,γ,δ ≥ 0 and ϱ:= γβ + αγ + αδ > 0. Let ψ(t) = β + αt, ϕ(t) = γ + δ - γt, t ∈ [0,1]. We study the existence of positive solutions for the m-point boundary value problem
⎧u” + h(t)f(u) = 0, 0 < t < 1,
⎨
⎩,
where , (for i ∈ 1,…,m-2) are given constants satisfying , and
.
We show the existence of positive solutions if f is either superlinear or sublinear by a simple application of a fixed point theorem in cones. Our result extends a result established by Erbe and Wang for two-point...
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