29 citations · 32 across the 4 of their papers we have counts for
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math.FA2017
Existence and stability of periodic solutions in a neural field equation
Karina Kolodina, Vadim Kostrykin, Anna Oleynik
We study the existence and linear stability of stationary periodic solutions to a neural field model, an intergo-differential equation of the Hammerstein type. Under the assumption…
math.FA2013
Iterative Schemes for Bump Solutions in a Neural Field Model
Anna Oleynik, Arcady Ponosov, John Wyller
We develop two iteration schemes for construction of localized stationary solutions (bumps) of a one-population Wilson-Cowan model with a smoothed Heaviside firing rate function. T…
math.FA2012★ 29 cited
An intermediate value theorem in ordered Banach spaces
Vadim Kostrykin, Anna Oleynik
We consider a monotone increasing operator in an ordered Banach space having and as a strong super- and subsolution, respectively. In contrast with the well studied cas…