Uniqueness and Parameter Dependence of Solutions of Fourth-order Four-point Nonhomogeneous Bvps

In this article, we investigate the fourth-order four-point nonhomogeneous Sturm-Liouville boundary-value problem u(t) = f(t, u(t)), t ∈ [0, 1], αu(0)− βu′(0) = γu(1) + δu′(1) = 0, au(ξ1)− bu(ξ1) = −λ, cu(ξ2) + du(ξ2) = −μ, where 0 ≤ ξ1 < ξ2 ≤ 1 and λ and μ are nonnegative parameters. We obtain sufficient conditions for the existence and uniqueness of positive solutions. The dependence of the solution on the parameters λ and μ is also studied.