Existence and uniqueness of positive periodic solutions for a class of integral equations with mixed monotone nonlinear terms

We study the existence and the uniqueness of positive periodic solutions for a class of integral equationsof the form ϕ(x)=∫[x,x+ω]∩GK(x,y)[f1(y,ϕ(y−τ(y)))+f2(y,ϕ(y−τ(y)))]dy,x∈G,where G is a closed subset of RN with periodic structure. Our analysis relies on the fixed point theory for mixed monotone operator in Banach space.