67 citations · 251 across the 15 of their papers we have counts for
15 papers
On the non-uniqueness of continuous solutions to differential equations with a discrete state-dependent delay
Alexander Rezounenko
We discuss the non-uniqueness of continuous solutions to differential equations with a {\it discrete } state-dependent delay and continuous initial functions. We are interested not…
Stability of a retrovirus dymanic model
Andrei Korobeinikov, Alexander Rezounenko
A retrovirus dynamic model is proposed. We pay attention to the case when viral pathogenicity is low and the infected cells are able to reproduce. Using Lyapunov function method we…
Viral infection model with diffusion and state-dependent delay: stability of classical solutions
Alexander Rezounenko
A class of reaction-diffusion virus dynamics models with intracellular state-dependent delay and a general non-linear infection rate functional response is investigated. We are int…
Stability of a viral infection model with state-dependent delay, CTL and antibody immune responses
Alexander Rezounenko
A virus dynamics model with intracellular state-dependent delay and nonlinear infection rate of Beddington-DeAngelis functional response is studied. The technique of Lyapunov funct…
Finite-dimensional global attractors for parabolic nonlinear equations with state-dependent delay
Igor Chueshov, Alexander Rezounenko
We deal with a class of parabolic nonlinear evolution equations with state-dependent delay. This class covers several important PDE models arising in biology. We first prove well-p…
Parabolic partial differential equations with discrete state-dependent delay: classical solutions and solution manifold
Tibor Krisztin, Alexander Rezounenko
Classical solutions to PDEs with discrete state-dependent delay are studied. We prove the well-posedness in a set which is an analogous to the solution manifold used for ordi…