Positive solutions for 2p-order and 2q-order nonlinear ordinary differential systems

In this paper, by using Krasnosel’skii fixed point theorem and under suitable conditions, we present the existence of single and multiple positive solutions to the following systems: ⎧⎪ ⎪⎪⎨⎪ ⎪⎪⎩ (−1)pu(2p) = λa(t)f (u(t), v(t)), t ∈ [0, 1], (−1)qv(2q) = μb(t)g(u(t), v(t)), t ∈ [0, 1], u(2i)(0) = u(2i)(1) = 0, 0 i p −1, v(2j)(0) = v(2j)(1) = 0, 0 j q − 1, where λ > 0, μ > 0, p, q ∈ N. We derive two explicit intervals of λ and μ such that for any λ and μ in the two intervals respectively, the existence of at least one solution to the systems is guaranteed, and the existence of at least two solutions for λ and μ in appropriate intervals is also discussed. © 2006 Elsevier Inc. All rights reserved