On the uniqueness of positive solution of an elliptic equation

This work deals with the uniqueness of positive solution for an elliptic equation whose nonlinearity satisfies an specific monotony property. In order to prove the main result, we employ a change of variable used in previous papers and the maximum principle.Ministerio de Ciencia y Tecnologí

Estudio teórico de un modelo simplificado sobre angiogénesis

En esta comunicación presentamos un sistema en ecuaciones en derivadas parciales no lineales simplificado que modela un proceso básico en el crecimiento tumores: la angiogénesis. Presentamos resultados de existencia de solución positiva del sistema estacionario en función de los parámetros del sistema

On the existence and multiplicity of positive solutions for some indefinite nonlinear eigenvalue problem

This paper concerns with the existence, uniqueness and/or multiplicity, and stability of positive solutions of an indefinite weight elliptic problem with concave or convex nonlinearity. We use mainly bifurcation method to obtain our results.Ministerio de Ciencia y Tecnologí

Stability and uniqueness for cooperative degenerate Lotka-Volterra model

In this work we deal with the existence, stability and uniqueness of positive solution of the symbiotic Lotka-Volterra degenerate model. We study and characterize the existence of the principal eigenvalue for weakly coupled elliptic cooperative singular systems. We use it, monotony methods and blowing up arguments to get our results and to show the change of behaviour between the cases of weak and strong mutualism and between non-degenerate and degenerate model.Comisión Interministerial de Ciencia y Tecnologí

Cooperative systems with any number of species

In this paper we study the positive solutions of a cooperative system of any number of equations which considers the case of the slow diffusion and includes the Lotka-Volterra model. We determine conditions of existence of global solution and blow-up in finite time in term of the value of the spectral radius of a certain nonnegative matrix associated to the system. The results generalize the ones known for the particular case of two equations and we justify them by using the specific properties of nonnegative matrices which translate the cooperative character of the system.Comisión Interministerial de Ciencia y Tecnologí

On the existence of dead cores for degenerate Lotka-Volterra models

In this work we study the existence, uniqueness and qualitative properties of nonnegative solutions of the Lotka-Volterra models with nonlinear diffusion under homogeneous Dirichlet boundary conditions. We consider the three typical interactions: prey-predator, competition and symbiosis. Unlike the linear diffusion models, nontrivial nonnegative solutions can exist which are not strictly positive. Sufficient conditions in terms of the coefficients involved in the setting of the models are given assuring that one species (or both) does not survive on a set of its habitat (called “dead core”) of positive measure.DGICY

Positive solutions for the degenerate logistic indefinite superlinear problem the slow diffusion case

In this work we study the existence, stability and multiplicity of the positive steady-states solutions of the degenerate logistic indefinite superlinear problem. By an adequate change of variable, the problem is transformed into an elliptic equation with concave and indefinite convex nonlinearities. We use singular spectral theory, the Leray-Schauder degree, bifurcation and monotony methods to obtain the existence results, and fixed point index in cones and a Picone identity to show the multiplicity results and the existence of a unique positive solution linearly asymptotically stable.Comisión Interministerial de Ciencia y TecnologíaMinisterio de Ciencia y Tecnologí

Positive solutions of a system arising from angiogenesis

We study a system of equations arising from angiogenesis which contains a nonregular term that vanishes below a certain threshold. This loss of regularity forces one to modify the usual methods of bifurcation theory. Nevertheless, we obtain results on the existence, uniqueness and permanence of a positive solution for the time-dependent problem; and the existence and uniqueness of a positive solution for the stationary one.Ministerio de Educación y Cienci

A non-local perturbation of the logistic equation in IR N

A logistic equation in the whole space is considered. In this problem, a non-local perturbation is included. We establish a new sub-supersolution method forgeneral nonlocal elliptic equations and, consequently, we obtain the existence ofpositive solutions of a nonlocal logistic equation.Ministerio de Economía y Competitividad (MINECO). EspañaEuropean Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER)Conselho Nacional de Desenvolvimento Científico e Tecnológico. BrasilCoordenação de Aperfeiçoamento de Pessoal de Nivel Superior. Brasi

Matrix Methods for the Dynamic Range Optimization of Continuous-TimeGm-CFilters

This paper presents a synthesis procedure for the optimization of the dynamic range of continuous-time fully differential G m - C filters. Such procedure builds up on a general extended state-space system representation which provides simple matrix algebra mechanisms to evaluate the noise and distortion performances of filters, as well as, the effect of amplitude and impedance scaling operations. Using these methods, an analytical technique for the dynamic range optimization of weakly nonlinear G m - C filters under power dissipation constraints is presented. The procedure is first explained for general filter structures and then illustrated with a simple biquadratic section