Existence of solutions to nonlinear first-order PBVPs on time scales

In this paper we are concerned with the following nonlinear first-order periodic boundary value problem on time scales {xΔ(t)+p(t)x(σ(t))=g(t,x(σ(t))),t∈[0,T]T,x(0)=x(σ(T)). Some new existence criteria of at least one solution are established by using novel inequalities and the well-known Schaefer fixed point theorem.