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Zbl 1173.47056
Dhage, Bapurao C.
Local asymptotic attractivity for nonlinear quadratic functional integral equations.
(English)
[J] Nonlinear Anal., Theory Methods Appl. 70, No. 5, A, 1912-1922 (2009). ISSN 0362-546X

The paper deals with the quadratic functional-integral equation of mixed type $$x(t)=[f(t,x(\alpha(t)))]\big(q(t)+\int_0^{\beta(t)}g(t,s,x(\gamma(s)))\,ds\big). \tag1$$ Using a result about operator equations in Banach algebras, the author proves the existence of a solution of (1) in the space $BC(\mathbb{R}_+,\mathbb{R})$. It is also proved that the solutions of (1) are uniformly locally asymptotically attractive on $\mathbb{R}_+$.
[Mirosława Zima (Rzeszow)]
MSC 2000:
*47N20 Appl. of operator theory to differential and integral equations
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
34K99 Functional-differential equations
45G10 Nonsingular nonlinear integral equations

Keywords: quadratic functional integral equation; fixed point theorem; uniformly locally asymptotically attractive solution

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