Positive solutions to nonlinear first-order PBVPs with parameter on time scales

In this paper we consider the following nonlinear first-order periodic boundary value problem with parameter on a time scale TT{xΔ(t)+p(t)x(σ(t))=λf(x(t)),t∈[0,T]T,x(0)=x(σ(T)),where λ>0λ>0 is a parameter. For suitable λ>0λ>0, some existence, multiplicity and nonexistence criteria of positive solutions are established by using well-known results from the fixed-point index.