4 papers
A fixed-point theorem for local operators with applications to stochastic equations
Arcady Ponosov
We study weak and strong solutions of nonlinear non-compact operator equations in abstract spaces of adapted random points. The main result of the paper is similar to Schauder's fi…
On wellposedness of generalized neural field equations with delay
Evgenii Burlakov, Evgeny Zhukovskiy, Arcady Ponosov +1
We obtain conditions for existence of unique global or maximally extended solutions to generalized neural field equations. We also study continuous dependence of these solutions on…
Spatially localized solutions of the Hammerstein equation with sigmoid type of nonlinearity
Anna Oleynik, Arcady Ponosov, Vadim Kostrykin +1
We study the existence of fixed points to a parameterized Hammertstain operator $\cH_β,$ with sigmoid type of nonlinearity. The parameter indicates th…
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…