19 citations · 57 across the 4 of their papers we have counts for
6 papers
Linearization and invariant manifolds on the carrying simplex for competitive maps
Janusz Mierczyński, Lei Niu, Alfonso Ruiz-Herrera
A folklore result due to M.W. Hirsch states that most competitive maps admit a carrying simplex, i.e., an invariant hypersurface which attracts all nontrivial orbits. The common ap…
Lyapunov exponents and Oseledets decomposition in random dynamical systems generated by systems of delay differential equations
Janusz Mierczyński, Sylvia Novo, Rafael Obaya
Linear skew-product semidynamical systems generated by random systems of delay differential equations are considered, both on a space of continuous functions as~well as on a space…
Globally positive solutions of linear parabolic partial differential equations of second order with Dirichlet boundary conditions
Janusz Mierczyński
It is shown that globally positive solutions of a linear second order parabolic partial differential equation on a bounded domain, with Dirichlet boundary conditions, are unique up…
Time averaging for nonautonomous/random linear parabolic equations
Janusz Mierczyński, Wenxian Shen
Linear nonautonomous/random parabolic partial differential equations are considered under the Dirichlet, Neumann or Robin boundary conditions, where both the zero order coefficient…
Globally positive solutions of linear parabolic PDE's of second order with Robin boundary conditions
Janusz Mierczyński
It is shown that globally positive solutions of a linear second order parabolic partial differential equation on a bounded domain, with Robin boundary conditions, are unique up to…
On smoothness of carrying simplices
Janusz Mierczyński
We consider dissipative strongly competitive systems of ordinary differential equations. It is known that for a wide class of such systems there exists…