RODRÍGUEZ BERNAL , Aníbal

Damos condiciones finas sobre el tamaño y la forma de una perturbación que consigue que un problema lineal no autónomo pase de ser neutralmente estable a exponencialmente estable. Estos resultados se aplican al estudio del comportamiento asintótico de ecuaciones logísticas no autónomas.

The aim of this paper is to provide a comprehensive study of some linear non-local diffusion problems in metric measure spaces. These include, for example, open subsets in ℝN, graphs, manifolds, multi-structures and some fractal sets. For this, we study regularity, compactness, positivity and the spectrum of the stationary non-local operator....

In this paper we analyse the asymptotic behaviour of some nonlocal diffusion problems with local reaction term in general metric measure spaces. We find certain classes of nonlinear terms, including logistic type terms, for which solutions are globally defined with initial data in Lebesgue spaces. We prove solutions satisfy maximum and...

The book contains a selection of contributions given at the 23th Congress on Differential Equations and Applications (CEDYA) / 13th Congress of Applied Mathematics (CMA) that took place at Castellon, Spain, in 2013. CEDYA is renowned as the congress of the Spanish Society of Applied Mathematics (SEMA) and constitutes the main forum and meeting...

In this paper we study in detail the geometrical structure of global pullback and forwards attractors associated to non-autonomous Lotka-Volterra systems in all the three cases of competition, symbiosis or prey-predator. In particular, under some conditions on the parameters, we prove the existence of a unique non-degenerate global solution for...

Estudiamos la dinámica de una ecuación de reacción difusión que presenta una discontinuidad. En primer lugar probamos la semicontinuidad superior del atractor con respecto a aproximaciones suaves del término no lineal. Después damos una descripción precisa del conjunto de puntos fijos y su estabilidad. Finalmente, analizamos las posibles...

In this paper we study in detail the pullback and forwards attractions to non-autonomous competition Lotka-Volterra system. In particular, under some conditions on the parameters, we prove the existence of a unique non-degenerate global solution for these models, which attracts any other complete bounded trajectory. For that we present...

Analizamos la existencia de puntos de retroceso y de soluciones resonantes en un problema elíptico con condición de frontera no lineal dependiente de un parámetro del tipo ∂u ∂n = λu+g(λ, x, u) de forma que g es oscilatoria y g(λ,x,u) u → 0 cuando |u| → ∞. Existen ramas no acotadas de soluciones que no son a priori ni subcríticas ni...

Lotka-Volterra systems are the canonical ecological models used to analyze population dynamics of competition, symbiosis or prey-predator behaviour involving different interacting species in a fixed habitat. Much of the work on these models has been within the framework of infinite-dimensional dynamical systems, but this has frequently been...

The goal of this work is to study the forward dynamics of positive solutions for the nonautonomous logistic equation ut − ∆u = λu − b(t)up, with p > 1, b(t) > 0, for all t ∈ R, limt→∞ b(t) = 0. While the pullback asymptotic behaviour for this equation is now well understood, several different possibilities are realised in the forward asymptotic regime.