Electronic Journal of Differential Equations,
Vol. 2019 (2019), No. 99, pp. 1-20.

Title: Avery fixed point theorem applied to Hammerstein integral equations

Authors: Paul W. Eloe (Univ. of Dayton, Dayton, OH, USA)
         Jeffrey T. Neugebauer (Eastern Kentucky Univ., Richmond, KY, USA)
 
Abstract:
 We apply a recent Avery et al. fixed point theorem to the Hammerstein
 integral equation
 $$
 x(t)=\int^{T_2}_{T_1}G(t,s)f(x(s))\,ds, \quad t\in[T_1,T_2].
 $$
 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.