arXiv subjects
Publications and source records attributed to Julián Epstein.
An abstract version of the celebrated inequality is described by means of the spectral bound of an operator defined on a Banach lattice. As a consequence, uniqueness and continuous dependence results for the general semilinear problem $Lu=N(u)$ are established and a connection with the maximum principle is explored.
An abstract formulation of a duality principle established by Krasnoselskii is presented. Under appropriate conditions, it shall be shown that, if the solutions of a nonlinear functional equation can be obtained by finding fixed points of certain operators in possibly different Banach spaces, then these operators share some topological properties.
The main purpose of this paper is to study the existence of periodic solutions for a nonautonomous differential-difference system describing the dynamics of hematopoietic stem cell (HSC) population under some external periodic regulatory factors at the cellular cycle level. The starting model is a nonautonomous system of two age-structured partial differential equations describing the HSC population in quiescent ($G_0$) and proliferating ($G_1$, $S$, $G_2$ and $M$) phase. We are interested on the effects of a periodically time varying coefficients due for example to circadian rhythms or to the periodic use of certain drugs, on the dynamics of HSC population. The method of characteristics reduces the age-structured model to a nonautonomous differential-difference system. We prove under appropriate conditions on the parameters of the system, using topological degree techniques and fixed point methods, the existence of periodic solutions of our model.
Motivated by Lazer-Leach type results, we study the existence of periodic solutions for systems of functional-differential equations at resonance with an arbitrary even-dimensional kernel and linear deviating terms involving a general delay of the form $\int_0^{2π}u(t+s)\,dλ(s)$, where $λ$ is a finite regular signed measure. Our main technique shall be the Coincidence Degree Theorem due to Mawhin.