Positive solutions for nonlinear m-point eigenvalue problems

In this paper, we are concerned with determining values of λ, for which there exist positive solutions of the nonlinear eigenvalue problem    (p(t)u ) − q(t)u +λh(t)f (u) = 0, 0 < t <1, au(0) − bp(0)u (0) = m−2 i=1 αiu(ξi ), cu(1) + dp(1)u (1) = m−2 i=1 βiu(ξi ), where a, b, c, d ∈ [0,∞), ξi ∈ (0, 1), αi,βi ∈ [0,∞) (for i ∈ {1, . . . , m − 2}) are given constants, p, q ∈ C([0, 1], (0,∞)), h ∈ C([0, 1], [0,∞)), and f ∈ C([0,∞), [0,∞)) satisfying some suitable conditions. Our proofs are based on Guo–Krasnoselskii fixed point theorem.  2004 Elsevier Inc. All rights reserved.