Existence of positive, negative and sign-changing periodic solutions for a class of integral equations

In this paper, the simultaneous existence of positive, negative and sign-changing periodic solutions for a class of integral equations of the form ϕ(x)=∫[x,x+ω]∩ΩK(x,y)f(y,ϕ(y−τ(y)))dy,x∈Ω, is considered, where ΩΩ is a closed subset of RNRN with a periodic structure. Our main result is different from most existing results since they provide three constant sign periodic solutions only.