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Solutions of Hammerstein equations in the space BV (I<sup>b</sup><inf>a</inf>)

Abstract:

where a = (a1, a2), b = (b1, b2) ∈ ℝ2, (Figure presented.) = [a1, b1]×[a2, b2], 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.)).