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

In this paper, we investigate the following nonlinear first-order three-point boundary value problem on time scale TT: View the MathML source{xΔ(t)+p(t)x(σ(t))=f(t,x(σ(t))),t∈[0,T]T,x(0)−αx(ξ)=βx(σ(T)). Turn MathJax on 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.