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In this paper, we consider the following p-Laplacian multipoint boundary value problem on time scales:where φ p (s) = |s| p−2 s, p > 1, ξ i ∈ [0, T ] T , 0 < ξ 1 < ξ 2 < · · · < ξ n−2 < ρ(T ). By using fixed point index, we provide some sufficient conditions for the existence of multiple positive solutions to the above boundary value problem. Especially, the nonlinear term f (t, u) is allowed to change sign. As an application, an example is given to demonstrate our result.

In this paper, by using fixed point theorem, we prove the existence of multiple positive solutions for a class of nth-order p-Laplacian m-point singular boundary value problem. The interesting point is that the nonlinear term f explicitly involves the each-order derivative of variable u(t).Keywords p-Laplacian operator · nth-order m-point singular boundary value problem · Positive solutions · Fixed points Mathematics Subject Classification (2000) 34B10 · 34B16 · 34B18

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