Avery fixed point theorem applied to Hammerstein integral equations
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Date
2019-08-13
Authors
Eloe, Paul W.
Neugebauer, Jeffrey T.
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We 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.
Description
Keywords
Hammerstein integral equation, Boundary-value problem, Fractional boundary-value problem
Citation
Eloe, 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.
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Attribution 4.0 International
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This work is licensed under a Creative Commons Attribution 4.0 International License.