Anti-periodic boundary value problem for first order dynamic equations on time scales

In this paper we are concerned with the following first order anti-periodic boundary value problem on time scale T {x^Δ(t) + λx(σ(t)) = f(t, x(σ(t))), t ϵ [0, T], x(0) = -x(σ(T)), where λ >; 0 is a parameter and f : [0, T]×R → R is continuous. Some existence criteria are established by using a Leray-Schauder nonlinear alternative.