Positive solution for m-point boundary value problems of fourth order

In this paper, we consider the existence of positive solutions to the fourth order boundary value problem ⎧⎪ ⎨⎪ ⎩ u +αu −βu = f (t,u), 0 < t <1, u(0) = m−2 i=1 aiu(ξi ), u(1) = m−2 i=1 biu(ξi ), u (0) = m−2 i=1 aiu (ξi ), u (1) = m−2 i=1 biu (ξi ), where α,β ∈ R, ξi ∈ (0, 1), ai, bi ∈ [0,∞) for i ∈ {1, 2, . . . , m − 2} are given constants satisfying some suitable conditions. The proofs are based on the fixed point index theorem in cones. © 2005 Elsevier Inc. All rights reserved.