Solutions of Hammerstein equations in the spaceBV()
Wadie Aziz, Hugo Leiva, Nelson Merentes · Quaestiones Mathematicae · 2014
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 ( ).