Positive solutions to a generalized second-order three-point boundary-value problem on time scales

Abstract

Let T be a time scale with 0, T ∈ T. We investigate the existence and multiplicity of positive solutions to the nonlinear second-order three-point bounary-value problem u∆∇(t) + α(t)ƒ (u(t)) = 0, t ∈ [0, T] ⊂ T, u(0) = βu(η), u(T) = αu(η) on time scales T, where 0 < η < T, 0 < α < T/η, 0 < β < T-αη / T-η are given constraints.