In this paper, we investigate the existence of multiple positive solutions for the following fourthorder p-Laplacian Sturm-Liouville boundary value problems on time scales ﹛[φp（u^△△（t））]^△△= f（t, u（σ（t）））, t ∈ [a, b],α0 u（a）- β0u^△（a） = 0, γ0 u（σ（b）） ＋ δ0 u△（σ（b）） = 0,α0（φp（u^△△））（a）- β0（φp（u^△△））△（a） = 0,γ0（φp（u^△△））（σ（b）） ＋ δ0（φp（u^△△））△（σ（b）） = 0,where φp（s） is the p-Laplacian operator. Under growth conditions on the nonlinearity f some existence results of at least two and three positive solutions for the above problem are obtained by virtue of fixed point theorems on cone. In particular, the nonlinearity f may be both sublinear and superlinear.
In this paper, by virtue of Leray-Lions theorem, we are mainly concerned with the existence of weak solutions to a Dirichlet boundary value problem with the p-Laplacian operator.
