Rocky Mountain Journal of Mathematics

On existence and uniqueness of $L_1$-solutions for quadratic integral equations via a Krasnoselskii-type fixed point theorem

Ravi P. Agarwal, Mohamed M.A. Metwali, and Donal O'Regan

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Using a Krasnoselskii-type fixed point theorem due to Burton, we discuss the existence of integrable solutions of general quadratic-Urysohn integral equations on a bounded interval $(a,b)$. Uniqueness of the solution is also studied. An example to illustrate our theory is also included.

Article information

Rocky Mountain J. Math., Volume 48, Number 6 (2018), 1743-1762.

First available in Project Euclid: 24 November 2018

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Zentralblatt MATH identifier

Primary: 45G10: Other nonlinear integral equations 47H30: Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.) [See also 45Gxx, 45P05] 47N20: Applications to differential and integral equations

Quadratic-Urysohn integral equations integrable solutions Krasnoselskii's fixed point theorem uniqueness of the solution


Agarwal, Ravi P.; Metwali, Mohamed M.A.; O'Regan, Donal. On existence and uniqueness of $L_1$-solutions for quadratic integral equations via a Krasnoselskii-type fixed point theorem. Rocky Mountain J. Math. 48 (2018), no. 6, 1743--1762. doi:10.1216/RMJ-2018-48-6-1743.

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