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Existence of monotone solutions for a nonlinear quadratic integral equation of Volterra type. (English) Zbl 1147.45005
A sufficient condition for the existence of monotone solutions of the following nonlinear quadratic integral equation of Volterra type $$x(t)= a(t)+ g(x(t)) \int_0^t v(t,s,x(s))\, \quad\text{for all }t\in[0,T],$$ is established. The approach is based on Darbo’s fixed point theorem and the measure of noncompactness introduced by {\it J. Banaś} and {\it L. Olszowy} [in Ann. Soc. Math. Pol., Ser. I, Commentat. Math. 41, 13--23 (2001; Zbl 0999.47041)].

45G10Nonsingular nonlinear integral equations
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
47H09Mappings defined by “shrinking” properties
Full Text: DOI Euclid
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