We study the following third-order p-Laplacian m-point boundary value problems on time scales: φp uΔ∇ ∇ a t f t, u t 0, t ∈ 0, T T, βu 0 − γuΔ 0 0, u T ∑m−2 i 1 aiu ξi , φp u Δ∇ 0 ∑m−2 i 1 biφp u Δ∇ ξi , where φp s is p-Laplacian operator, that is, φp s |s|p−2s, p > 1, φ−1 p φq, 1/p 1/q 1, 0 < ξ1 < · · · < ξm−2 < ρ T . We obtain the existence of positive solutions by using fixed-point theorem i...

Abstract This paper derives several sufficient conditions for the existence of three solutions to Dirichlet problem a second-order self-adjoint difference equation involving p -Laplacian through critical point theory. Furthermore, by using strong maximum principle, we prove that are positive under appropriate assumptions on nonlinearity. Finally, present examples confirm our results.