Electron. J. Differential Equations, Vol. 2019 (2019), No. 99, pp. 1-20.

Avery fixed point theorem applied to Hammerstein integral equations

Paul W. Eloe, Jeffrey T. Neugebauer

We apply a recent Avery et al. fixed point theorem to the Hammerstein integral equation

Under certain conditions on G, we show the existence of positive and positive symmetric solutions. Examples are given where G is a convolution kernel and where G is a Green's function associated with different boundary-value problem.

Submitted November 28, 2018. Published August 13, 2019.
Math Subject Classifications: 47H10, 34A08, 34B15, 34B27, 45G10.
Key Words: Hammerstein integral equation; boundary-value problem; fractional boundary-value problem.

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Paul W. Eloe
Department of Mathematics
University of Dayton
Dayton, OH 45469, USA
email: peloe1@udayton.edu
Jeffrey T. Neugebauer
Department of Mathematics and Statistics
Eastern Kentucky University
Richmond, KY 40475, USA
email: Jeffrey.Neugebauer@eku.edu

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