Existence of solution and positive solution of BVP for nonlinear third-order dynamic equation

In this paper we are concerned with the following third-order two-point boundary value problem on time scale TTuΔΔΔ(t)+f(t,u(t),uΔΔ(t))=0,t∈[a,ρ(b)],u(a)=A,u(σ2(b))=B,uΔΔ(a)=C.Some existence criteria of solution and positive solution are established by using Leray–Schauder fixed point theorem and our main conditions are local. An example is also included to illustrate the importance of the results obtained.