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Zbl 1147.45005
Liu, Zeqing; Kang, Shin Min
Existence of monotone solutions for a nonlinear quadratic integral equation of Volterra type.
(English)
[J] Rocky Mt. J. Math. 37, No. 6, 1971-1980 (2007). ISSN 0035-7596

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)].
[Jürgen Appell (Würzburg)]
MSC 2000:
*45G10 Nonsingular nonlinear integral equations
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
47H09 Mappings defined by "shrinking" properties

Keywords: nonlinear quadratic integral equation of Volterra type; monotone solution; Darbo's fixed point theorem; measure of noncompactness

Citations: Zbl 0999.47041

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