Let T be a time scale such that 0, T ∈ T. Consider the following three-point boundary value problem on time scales: uΔ∇(t) + a(t)f(t,u(t)) = 0, t ∈ (0,T), β u(0) - γuΔ(0) = 0, αu(η) = u(T), where β, γ ≥ 0, β + γ > 0, η ∈ (0, ρ(T)), 0 < α < T/η, and d = β (T - α η) + γ (1 - α) > 0. By using fixed point theorems in cones, some new and general results are obtained for the existence of single and multiple positive solutions of the above problem. In particular, our criteria generalize and improve some known results. © 2004 Published by Elsevier Inc.
Sun, H. R., & Li, W. T. (2004). Positive solutions for nonlinear three-point boundary value problems on time scales. Journal of Mathematical Analysis and Applications, 299(2), 508–524. https://doi.org/10.1016/j.jmaa.2004.03.079