Solutions of the Hammerstein equations in BVφ(IAB,R)
Journal Title: Discussiones Mathematicae Differential Inclusions Control and Optimization - Year 2016, Vol 36, Issue 2
Abstract
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))dy in the space of function of bounded total φ-variation in the sense of Hardy-Vitali-Tonelli, where λϵR, K:I_a^b× I_a^b→ R and f:I_a^b× R→R 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.
Authors and Affiliations
Wadie Aziz, José A. Guerrero, L. Antonio Azócar, Nelson Merentes
Keywords
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