Abstract :
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
