Wadie Aziz ; José A. Guerrero ; L. Antonio Azócar ; Nelson Merentes

Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 36 (2016), p. 207-229 / Harvested from The Polish Digital Mathematics Library

Résumé

In this paper we study existence and uniqueness of solutions for the Hammerstein equation u(x)=v(x)+λ∫IabK(x,y)f(y,u(y))dy in the space of function of bounded total $\varphi $-variation in the sense of Hardy-Vitali-Tonelli, where $\lambda \in \mathbb {R}$, $K:I_a^b\times I_a^b \longrightarrow \mathbb {R}$ and $f:I_a^b\times \mathbb {R} \longrightarrow \mathbb {R}$ 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.

Détail

Publié le : 2016-01-01
EUDML-ID : urn:eudml:doc:289597

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