Positive Solutions for Third-Order p-Laplacian Functional Dynamic Equations on Time Scales

Let T be a closed nonempty subset of R, and let T have the subspace topology inherited from the Euclidean topology on R. In some of the current literature, T is called a time scale or measure chain . For notation, we shall use the convention that, for each interval of J of R, J will denote time scales interval, that is, J : J ∩ T. In this paper, let T be a time scale such that −r, 0, T ∈ T. We are concerned with the existence of positive solutions of the p-Laplacian dynamic equation on a time scale [ φp ( xΔ∇ t )]∇ a t f ( x t , x ( μ t )) 0, t ∈ 0, T ,