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Wadie AzizJosé A. GuerreroL. Antonio AzócarNelson Merentes — 2016

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper we study existence and uniqueness of solutions for the Hammerstein equation u ( x ) = v ( x ) + λ I a b K ( x , y ) f ( y , u ( y ) ) d y in the space of function of bounded total ϕ -variation in the sense of Hardy-Vitali-Tonelli, where λ , K : I a b × I a b and f : I a b × are suitable functions. The existence and uniqueness of solutions are proved by means of the Leray-Schauder nonlinear alternative and the Banach contraction mapping principle.

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