Let T ⊆ R be a time scale. The purpose of this paper is to present sufficient conditions for the existence of multiple positive solutions of the following Lidstone boundary value problem on time scales (−1)nyΔ(2n)(t) = f(t, y(t)), t ∈ [a, b]T, yΔ(2i)(a) = yΔ(2i)(σ2n−2i(b)) = 0 i = 0, 1, ..., n − 1. Existence of multiple positive solutions are established using fixed point methods. At the end some examples are also given to illustrative our results.
Mathematics Subject Classification 34N05;34K10; 39A10; 39A99