Multiple positive solutions of nonlinear third-order BVP for a class of pp-Laplacian dynamic equations on time scales

In this paper, by using fixed-point theorems in cones, the existence of multiple positive solutions is considered for singular nonlinear boundary value problem for the following third-order pp-Laplacian dynamic equations on time scales (Φp(uΔΔ(t)))∇+f(t,u(t))=0,t∈[a,b],αu(ρ(a))−βuΔ(ρ(a))=0,γu(b)+δuΔ(b)=0,uΔΔ(ρ(a))=0, where Φp(s)Φp(s) is pp-Laplacian operator, i.e., Φp(s)=|s|p−2s,p>1,Φp−1=Φq,1p+1q=1. In particular, the conditions we used in the paper are different from those in [R.Y. Ma, Existence of solutions of nonlinear mm-point boundary value problem, J. Math. Anal. Appl. 256 (2001) 556–567; A.M. Mao, S.X. Luan, Y.H. Ding, On the existence of positive solutions for a class of singular boundary value problems, J. Math. Appl. 298 (2004) 57–72].