Now showing items 1-20 of 85

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      A logistic equation with degenerate diffusion and Robin boundary condition  [Article]

      Suárez Fernández, Antonio (American Institute of Mathematical Sciences, 2008-09)
      In this paper we study a model for a species confined in a bounded region. This species diffuses slowly, follows a logistic law in the habitat and there is a flux of population across the boundary of the habitat. Basically, ...
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      A Lotka-Volterra symbiotic model with cross-diffusion  [Article]

      Delgado Delgado, Manuel; Da Silva Montenegro, Marcelo; Suárez Fernández, Antonio (Elsevier, 2009-03-01)
      The main goal of this paper is to study the existence and non-existence of coexistence states for a Lotka-Volterra symbiotic model with cross-diffusion. We use mainly bifurcation methods and a priori bounds to give sufficient ...
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      A non-local perturbation of the logistic equation in IR N  [Article]

      Delgado Delgado, Manuel; Molina Becerra, Mónica; Rodrigues dos Santos Júnior, Joao; Suárez Fernández, Antonio (Elsevier, 2019-10)
      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 ...
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      A nonlinear age-dependent model with spatial diffusion  [Article]

      Delgado Delgado, Manuel; Molina Becerra, Mónica; Suárez Fernández, Antonio (Elsevier, 2006-01-01)
      The main goal of this paper is to study the existence and uniqueness of positive solution for a nonlinear age-dependent equation with spatial diffusion. For that, we mainly use properties of an eigenvalue problem related ...
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      A sub-supersolution method for nonlinear elliptic singular systems with natural growth and some applications  [Article]

      Carmona Tapia, José; Martínez Aparicio, Pedro Jesús; Suárez Fernández, Antonio (Elsevier, 2016-02)
      In this paper we give a sub-supersolution method for nonlinear elliptic singular systems with quadratic gradient whose model system is the following where Ω is a smooth bounded domain of RN (N≥3), β,μ≥0, 0<α,γ<1 and regular ...
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      A variational approach to a nonlocal elliptic problem with sign-changing nonlinearity  [Article]

      Sobreira de Araujo Correa, Francisco Júlio; Delgado Delgado, Manuel; Suárez Fernández, Antonio (De Gruyter, 2011-05)
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      Age-dependent diffusive Lotka-Volterra type systems  [Article]

      Delgado Delgado, Manuel; Suárez Fernández, Antonio (Elsevier, 2007-03)
      In this paper it is shown that the sub-supersolution method works for age-dependent diffusive nonlinear systems with non-local initial conditions. As application, we prove the existence and uniqueness of positive solution ...
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      Algunos modelos de la dinámica de poblaciones  [Article]

      Suárez Fernández, Antonio (Sociedad Española de Matemática Aplicada, 2002)
      En este trabajo presentamos el estudio teórico de algunos modelos de ecuaciones en derivadas parciales que aparecen en la modelización de la dinámica de poblaciones
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      Algunos modelos estacionarios de dinámica de poblaciones estructurados en edad con difusión  [Presentation]

      Delgado Delgado, Manuel; Molina Becerra, Mónica; Suárez Fernández, Antonio (2004)
      En este trabajo, daremos algunos resultados de existencia y unicidad de solución para un problema de dinámica de poblaciones estructurado en edad con difusión. Primero describiremos un método de sub-supersolución para este ...
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      An angiogenesis model with nonlinear chemotactic response and flux at the tumor boundary  [Article]

      Delgado Delgado, Manuel; Gayte Delgado, María Inmaculada; Morales Rodrigo, Cristian; Suárez Fernández, Antonio (Elsevier, 2010-01-01)
      In this paper we consider a parabolic problem as well as its stationary counterpart of a model arising in angiogenesis. The problem includes a chemotaxis type term and a nonlinear boundary condition at the tumor boundary. ...
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      An eigenvalue problem for non-bounded quasi-linear operator  [Article]

      Carmona Tapia, José; Suárez Fernández, Antonio (Cambridge University Press, 2004-06)
      In this paper we study the eigenvalues associated with a positive eigenfunction of a quasilinear elliptic problem with a not necessarily bounded operator. For that, we use the bifurcation theory and obtain the existence ...
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      Analysis of an age-structured predator-prey model with disease in the prey  [Article]

      Delgado Delgado, Manuel; Molina Becerra, Mónica; Suárez Fernández, Antonio (Elsevier, 2006-09)
      We study a nonlinear predator-prey model in which the prey population is affected by a mild disease, but has an effect on the death-rate and is assumed to have age structure. We assume that the predator population grows ...
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      Análisis de algunos modelos de dinámica de poblaciones no lineales estructurados en edad y espacio  [Article]

      Delgado Delgado, Manuel; Molina Becerra, Mónica; Suárez Fernández, Antonio (Sociedad Española de Matemática Aplicada, 2005)
      En este trabajo estudiamos modelos de la dinámica de poblaciones estructurados en edad con difusión. Construiremos un método de subsupersolución y veremos que, efectivamente, bajo la hipótesis de la existencia de un par ...
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      Anti-angiogenic therapy based on the binding receptors  [Article]

      Delgado Delgado, Manuel; Morales Rodrigo, Cristian; Suárez Fernández, Antonio (American Institute of Mathematical Sciences, 2012-11)
      This paper deals with a nonlinear system of partial differential equations modeling the effect of an anti-angiogenic therapy based on an agent that binds specific receptors of the endothelial cells. We study the time-dependent ...
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      Attracting complex networks  [Chapter of Book]

      Guerrero Suárez, Giovanny Fabián; Langa Rosado, José Antonio; Suárez Fernández, Antonio (Springer, 2016)
      Real phenomena from different areas of Life Sciences can be described by complex networks, whose structure is usually determining their intrinsic dynamics. On the other hand, Dynamical Systems Theory is a powerful tool for ...
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      Bifurcation from zero of a complete trajectory for non-autonomous logistic PDEs  [Article]

      Langa Rosado, José Antonio; Robinson, James C.; Suárez Fernández, Antonio (World Scientific Publishing, 2005-08)
      In this paper we extend the well-known bifurcation theory for autonomous logistic equations to the non-autonomous equation ut − ∆u = λu − b(t)u 2 with b(t) ∈ [b0, B0], 0 < b0 < B0 < 2b0. In particular, we prove the ...
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      Bifurcations in non-autonomous scalar equations  [Article]

      Langa Rosado, José Antonio; Robinson, James C.; Suárez Fernández, Antonio (Elsevier, 2006-02)
      In a previous paper we introduced various definitions of stability and instability for non-autonomous differential equations, and applied these to investigate the bifurcations in some simple models. In this paper we ...
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      Biodiversity and vulnerability in a 3D mutualistic system  [Article]

      Guerrero Suárez, Giovanny Fabián; Langa Rosado, José Antonio; Suárez Fernández, Antonio (American Institute of Mathematical Sciences, 2014-10)
      In this paper we study a three dimensional mutualistic model of two plants in competition and a pollinator with cooperative relation with plants. We compare the dynamical properties of this system with the associated ...
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      Characterization of non-autonomous attractors of a perturbed infinite-dimensional gradient system  [Article]

      Carvalho, Alexandre Nolasco; Langa Rosado, José Antonio; Robinson, James C.; Suárez Fernández, Antonio (Elsevier, 2007-05-15)
      In this paper we determine the exact structure of the pullback attractors in non-autonomous problems that are perturbations of autonomous gradient systems with attractors that are the union of the unstable manifolds of a ...