arXiv subjects
Publications and source records attributed to Antonio Suárez.
In this paper we deal with an eigenvalue problem in an interface elliptic equation. We characterize the set of principal eigenvalues as a level set of a concave and regular function. As application, we study a problem arising in population dynamics. In these problems each species lives in a subdomain, and they interact in a common border, which acts as a geographical barrier.
In this work we consider three species competing with each other in the same habitat. One of the species lives in the entire habitat, competing with the other two species, while the other two inhabit two disjoint regions of the habitat. These two populations just interact on a region/interface which acts as a geographical barrier. This barrier condition causes a drastic change in species behaviour compared to the classical Lotka-Volterra competitive model, showing very rich and new different situations depending on the several parameters involved in the system.
In this work we consider an interface logistic problem where two populations live in two different regions, separated by a membrane or interface where it happens an interchange of flux. Thus, the two populations only interact or are coupled through such a membrane where we impose the so-called Kedem-Katchalsky boundary conditions. For this particular scenario we analyze the existence and uniqueness of positive solutions depending on the parameters involve in the system, obtaining interesting results where one can see for the first time the effect of the membrane under such boundary conditions. To do so, we first ascertain the asymptotic behaviour of several linear and nonlinear problems for which we include a diffusion coefficient and analyse the behaviour of the solutions when such a diffusion parameter goes to zero or infinity. Despite their own interest, since these asymptotic results have never been studied before, they will be crucial in analyzing the existence and uniqueness for the main interface logistic problems under analysis. Finally, we apply such an asymptotic analysis to characterize the existence of solutions in terms of the growth rate of the populations, when both populations possess the same growth rate and, also, when they depend on different parameters.
Non-autonomous differential equations exhibit a highly intricate dynamics, and various concepts have been introduced to describe their qualitative behavior. In general, it is rare to obtain time dependent invariant compact attracting sets when time goes to plus infinity. Moreover, there are only a few papers in the literature that explore the geometric structure of such sets. In this paper we investigate the long time behaviour of cooperative $n$-dimensional non-autonomous Lotka-Volterra systems is population dynamics. We provide sufficient conditions for the existence of a globally stable (forward in time) entire solution in which one species becomes extinct, or where all species except one become extinct. Furthermore, we obtain the precise geometrical structure of the non-autonomous forward attractor in one, two, and three dimensions by establishing heteroclinic connections between the globally stable solution and the semi-stable solutions in cases of species permanence and extinction. We believe that understanding time-dependent forward attractors paves the way for a comprehensive analysis of both transient and long-term behavior in non-autonomous phenomena.
A class of generalized Schrödinger problems in bounded domain is studied. A complete overview of the set of solutions is provided, depending on the values assumed by parameters involved in the problem. In order to obtain the results, we combine monotony, bifurcation and variational methods.
In this paper we address the following Kirchhoff type problem \begin{equation*} \left\{ \begin{array}{ll} -Δ(g(|\nabla u|_2^2) u + u^r) = a u + b u^p& \mbox{in}~Ω, u>0& \mbox{in}~Ω, u= 0& \mbox{on}~\partialΩ, \end{array} \right. \end{equation*} in a bounded and smooth domain $Ω$ in ${\rm I}\hskip -0.85mm{\rm R}$. By using change of variables and bifurcation methods, we show, under suitable conditions on the parameters $a,b,p,r$ and the nonlinearity $g$, the existence of positive solutions.
In this paper we investigate a class of elliptic problems involving a nonlocal Kirchhoff type operator with variable coefficients and data changing its sign. Under appropriated conditions on the coefficients, we have shown existence and uniqueness of solution.