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Local asymptotic stability for nonlinear quadratic functional integral equations. (English) Zbl 1182.47058

Summary: In the present study, using characterizations of measures of noncompactness, we prove a theorem on the existence and local asymptotic stability of solutions for a quadratic functional integral equation via a fixed point theorem of Darbo. The investigations are placed in the Banach space of real functions defined, continuous and bounded on an unbounded interval. An example is indicated to demonstrate the natural realizations of the abstract result presented in the paper.

MSC:

47N20 Applications of operator theory to differential and integral equations
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47J05 Equations involving nonlinear operators (general)
45G10 Other nonlinear integral equations
34D05 Asymptotic properties of solutions to ordinary differential equations
34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
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