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Solutions of the Hammerstein equations in $BV_\varphi(I_{a}^{b},\, \mathbb{R})

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Aziz W., Guerrero J., Azócar L., Merentes N.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

2016

tom 36

nr 2

207-229

In this paper we study existence and uniqueness of solutions for the Hammerstein equation \[ u(x)= v(x) + \lambda \int_{I_{a}^{b}}K(x,y)f(y,u(y))dy \] \noi 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.

Ograniczanie wyników

1 Discussiones Mathematicae, Differential Inclusions, Control and Optimization

1 Aziz W.

1 Azócar L.

1 Guerrero J.

1 Merentes N.

1 2016

Wyniki wyszukiwania

Solutions of the Hammerstein equations in $BV_\varphi(I_{a}^{b},\, \mathbb{R})