Existence and uniqueness results for nonlinear first-order three-point boundary value problems on time scales

In this paper, we investigate the following nonlinear first-order three-point boundary value problem on time scale TT:{xΔ(t)+p(t)x(σ(t))=f(t,x(σ(t))),t∈[0,T]T,x(0)−αx(ξ)=βx(σ(T)). By using several well-known fixed point theorems, the existence of positive solutions is obtained. Besides, the uniqueness results are obtained by imposing growth restrictions on ff. In particular, Green’s function for the above boundary value problem is established.