431 citations · 1.1k across the 42 of their papers we have counts for
45 papers
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…
Diagonalization of indefinite saddle point forms
Luka Grubišić, Vadim Kostrykin, Konstantin A. Makarov +2
We obtain sufficient conditions that ensure block diagonalization (by a direct rotation) of sign-indefinite symmetric sesquilinear forms as well as the associated operators that ar…
The Tan -Theorem in Fluid Dynamics
Luka Grubišić, Vadim Kostrykin, Konstantin A. Makarov +2
We show that the generalized Reynolds number (in fluid dynamics) introduced by Ladyzhenskaya is closely related to the rotation of the positive spectral subspace of the Stokes bloc…
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…
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…
On the Existence of Unstable Bumps in Neural Networks
Vadim Kostrykin, Anna Oleynik
We study the neuronal field equation, a nonlinear integro-differential equation of Hammerstein type. By means of the Amann three fixed point theorem we prove the existence of bump…