Avery fixed point theorem applied to Hammerstein integral equations

Eloe, Paul W.Neugebauer, Jeffrey T.2021-12-012021-12-012019-08-13Eloe, P. W., & Neugebauer, J. T. (2019). Avery fixed point theorem applied to Hammerstein integral equations. <i>Electronic Journal of Differential Equations, 2019</i>(99), pp. 1-20.1072-6691https://hdl.handle.net/10877/14990We apply a recent Avery et al. fixed point theorem to the Hammerstein integral equation x(t) = ∫T2T1 G(t, s)ƒ(x(s)) ds, t ∈ [T1, T2]. 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.Text20 pages1 file (.pdf)enAttribution 4.0 InternationalHammerstein integral equationBoundary-value problemFractional boundary-value problemAvery fixed point theorem applied to Hammerstein integral equationsArticleThis work is licensed under a Creative Commons Attribution 4.0 International License.