On quadratic integral equations of Urysohn type in Fréchet spaces M Benchohra and M. A. Darwish Received: January 11, 2009; Accepted: May 8, 2009 Abstract. In this paper, we investigate the existence of a unique solution on a semiinfinite interval for a quadratic integral equation of Urysohn type in Fréchet spaces using a nonlinear alternative of Leray-Schauder type for contractive maps. Keywords: quadratic integral equation; existence and uniqueness; fixed-point; Leray-Schauder; Fréchet space. AMS Subject classification: Primary: 45G10, 45M99, 47H09 ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2008, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |