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Solutions of Hammerstein equations in the space BV (Ib a)

Abstract:

where a = (a<inf>1</inf>, a<inf>2</inf>), b = (b<inf>1</inf>, b<inf>2</inf>) ∈ ℝ<sup>2</sup>, (Figure presented.) = [a<inf>1</inf>, b<inf>1</inf>]×[a<inf>2</inf>, b<inf>2</inf>], v : (Figure presented.) → ℝ, k : (Figure presented.) × (Figure presented.) → ℝ, (Figure presented.) → ℝ, and f : (Figure presented.) × ℝ → ℝ. Under some conditions on λ, k and f we prove that this equation admits only one solution in the space BV ((Figure presented.)) for each v ∈ BV ((Figure presented.)).Abstract: In this paper we study the existence of solutions for Hammerstein integral equations in the space of two-variables bounded variation functions BV ((Figure presented.))(Figure presented.)