Solutions of Hammerstein equations in the space BV ()

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 = (a 1 , a 2 ), b = (b 1 , b 2 ) ∈ ℝ 2 , = [a 1 , b 1 ]×[a 2 , b 2 ], v : → ℝ, k : × → ℝ, → ℝ, and f : × ℝ → ℝ. Under some conditions on λ, k...

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Bibliographic Details
Published in:Quaestiones mathematicae 2014-01, Vol.37 (3), p.359-370
Main Authors: Aziz, W., Leiva, H., Merentes, N.
Format: Article
Language:English
Subjects:
Banach spaces
bounded variation
Hammerstein integral equation
Primary 93B05
Secondary 93C25
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Summary: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 = (a 1 , a 2 ), b = (b 1 , b 2 ) ∈ ℝ 2 , = [a 1 , b 1 ]×[a 2 , b 2 ], 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 ( ).
ISSN:1607-3606
1727-933X
DOI:10.2989/16073606.2014.894675