Avery fixed point theorem applied to Hammerstein integral equations
Eloe, Paul W.
Neugebauer, Jeffrey T.
Texas State University, Department of Mathematics
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.
Hammerstein integral equation, Boundary-value problem, Fractional boundary-value problem
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.