Nonlinear triple-point problems on time scales

Abstract

We establish the existence of multiple positive solutions to the nonlinear second-order triple-point boundary-value problem on time scales, u∆∇(t) + h(t)ƒ(t, u(t)) = 0, u(ɑ) = αu(b) + δu∆ (α), βu(c) + γu∆ (c) = 0 for t ∈ [α, c] ⊂ Τ, where Τ is a time scale, β, γ, δ ≥ 0 with β + γ > 0, 0 < α < c-α/ c-b and b ∈ (a, c) ⊂ T.