Existence and multiplicity of positive solutions for multi-parameter three-point differential equations system

In this paper, we study the existence and multiplicity of positive solutions for the differential equations system ⎧⎪ ⎪⎪⎨⎪ ⎪⎪⎩ x +λa1(t)f1(x(t ), y(t)) = 0, 0 < t <1, y +μa2(t)f2(x(t ), y(t)) = 0, 0 < t <1, x(0) = 0 = x(1)− α1x(η1), y(0) = 0 = y(1)− α2y(η2), where λ,μ > 0 are parameters, 0 < η2 η1 < 1, α1,α2 ∈ (0, 1), a1 ∈ C([0, 1], [0,∞)) and f2 ∈ C([0,∞)×[0,∞), [0,∞)). The system is a semi-positone problem since the nonlinear term f1 is allowed to take negative values and a2(t) may change sign on [0, 1]. The results are established via fixed point index theory. © 2005 Elsevier Inc. All rights reserved