Solutions of Hammerstein equations in the space BV ()

Abstract

In this paper we study the existence of solutions for Hammerstein integral equations in the space of two-variables bounded variation functions BV ()where a = (a1, a2), b = (b1, b2) ∈ ℝ2, = [a1, b1]×[a2, b2], v : → ℝ, k : × → ℝ, → ℝ, and f : × ℝ → ℝ. Under some conditions on λ, k and f we prove that this equation admits only one solution in the space BV () for each v ∈ BV ().