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Local asymptotic attractivity for nonlinear quadratic functional integral equations. (English) Zbl 1173.47056

The paper deals with the quadratic functional-integral equation of mixed type \[ x(t)=[f(t,x(\alpha(t)))]\big(q(t)+\int_0^{\beta(t)}g(t,s,x(\gamma(s)))\,ds\big). \tag{1} \] 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 \(\mathbb{R}_+\).

MSC:

47N20 Applications of operator theory to differential and integral equations
47H10 Fixed-point theorems
34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
45G10 Other nonlinear integral equations
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