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Displaying similar documents to “Normal integrands and related classes of functions”

Non-autonomous implicit integral equations with discontinuous right-hand side

Giovanni Anello, Paolo Cubiotti (2004)

Commentationes Mathematicae Universitatis Carolinae

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We deal with the implicit integral equation h ( u ( t ) ) = f ( t , ∫ I g ( t , z ) u ( z ) d z ) for a.a. t ∈ I , where I : = [ 0 , 1 ] and where f : I × [ 0 , λ ] → ℝ , g : I × I → [ 0 , + ∞ [ and h : ] 0 , + ∞ [ → ℝ . We prove an existence theorem for solutions u ∈ L s ( I ) where the contituity of f with respect to the second variable is not assumed.