Avery fixed point theorem applied to Hammerstein integral equations

Abstract

We apply a recent Avery et al. fixed point theorem to the Hammerstein integral equation x(t) = ∫T2T1 G(t, s)ƒ(x(s)) ds, t ∈ [T1, T2]. Under certain conditions on G, we show the existence of positive and positive symmetric solutions. Examples are given where G is a convolution kernel and where G is a Green's function associated with different boundary-value problem.