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2016 | 36 | 2 | 207-229
Tytuł artykułu

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

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Abstrakty
EN
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.
Twórcy
autor
  • Universidad de Los Andes Departamento de Física y Matemática Trujillo-Venezuela
  • Universidad Nacional Experimental del Táchira Departamento de Matemática y Física San Cristóbal-Venezuela
  • Universidad Nacional Abierta Area de Matem´atica, Caracas-Venezuela ´
  • Universidad Central de Venezuela Escuela de Matemáticas, Caracas-Venezuela
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Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1185
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