Positive solutions of second-order three-point boundary value problems with sign-changing coefficients

Ye Xue, Guowei Zhang
2016 Electronic Journal of Qualitative Theory of Differential Equations  
In this article, we investigate the boundary-value problem where β ≥ 0, η ∈ (0, 1), f ∈ C([0, ∞), [0, ∞)) is nondecreasing, and importantly h changes sign on [0, 1]. By the Guo-Krasnosel'skiȋ fixed-point theorem in a cone, the existence of positive solutions is obtained via a special cone in terms of superlinear or sublinear behavior of f . where λ is a positive parameter, η ∈ (0, 1), f ∈ C([0, ∞), [0, ∞)) is nondecreasing, δ ∈ (0, 1) and h(t) is continuous and especially changes sign on [0, 1]
more » ... nges sign on [0, 1] which is different from the nonnegative assumption in most of these studies. Karaca [4] studied the problems with more general boundary conditions x (t) + h(t) f (x(t)) = 0, t ∈ [0, 1], αx(0) = βx (0), x(1) = δx(η),
doi:10.14232/ejqtde.2016.1.97 fatcat:diy5tsgeq5aezldbmtl7r657he