- Tytuł:
- Solutions of the Hammerstein equations in $BV_\varphi(I_{a}^{b},\, \mathbb{R})
- Autorzy:
-
Aziz, Wadie
Guerrero, José
Azócar, L.
Merentes, Nelson - Powiązania:
- https://bibliotekanauki.pl/articles/729582.pdf
- Data publikacji:
- 2016
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
Hammerstein integral equation
Banach spaces
bounded $\varphi$-variation in the sense of Hardy-Vitali-Tonelli
Banach's contraction principle
Leray-Schauder nonlinear alternative principle - Opis:
- 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.
- Źródło:
-
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2016, 36, 2; 207-229
1509-9407 - Pojawia się w:
- Discussiones Mathematicae, Differential Inclusions, Control and Optimization
- Dostawca treści:
- Biblioteka Nauki
Artykuł