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

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2016)

  • Volume: 36, Issue: 2, page 207-229
  • ISSN: 1509-9407

Abstract

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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 ) ) d y in the space of function of bounded total ϕ -variation in the sense of Hardy-Vitali-Tonelli, where λ ∈ ℝ , 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.

How to cite

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Wadie Aziz, et al. "null." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 36.2 (2016): 207-229. <http://eudml.org/doc/289597>.

@article{WadieAziz2016,
abstract = {In this paper we study existence and uniqueness of solutions for the Hammerstein equation \[ u(x)= v(x) + \lambda \int \_\{I\_\{a\}^\{b\}\}K(x,y)f(y,u(y))dy \] 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.},
author = {Wadie Aziz, José A. Guerrero, L. Antonio Azócar, Nelson Merentes},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {Hammerstein integral equation; Banach spaces; bounded $\varphi $-variation in the sense of Hardy-Vitali-Tonelli; Banach's contraction principle; Leray-Schauder nonlinear alternative principle},
language = {eng},
number = {2},
pages = {207-229},
url = {http://eudml.org/doc/289597},
volume = {36},
year = {2016},
}

TY - JOUR
AU - Wadie Aziz
AU - José A. Guerrero
AU - L. Antonio Azócar
AU - Nelson Merentes
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2016
VL - 36
IS - 2
SP - 207
EP - 229
AB - In this paper we study existence and uniqueness of solutions for the Hammerstein equation \[ u(x)= v(x) + \lambda \int _{I_{a}^{b}}K(x,y)f(y,u(y))dy \] 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.
LA - eng
KW - Hammerstein integral equation; Banach spaces; bounded $\varphi $-variation in the sense of Hardy-Vitali-Tonelli; Banach's contraction principle; Leray-Schauder nonlinear alternative principle
UR - http://eudml.org/doc/289597
ER -

References

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