Carlos Velez | Universidad Nacional de Colombia (National University of Colombia) (original) (raw)

Papers by Carlos Velez

Boletín Científico CIOH, 2005

Resumen-El presente artículo presenta, en primera instancia, las ecuaciones de corrección de los ... more Resumen-El presente artículo presenta, en primera instancia, las ecuaciones de corrección de los datos de oleaje visual proporcionados por los barcos en ruta obtenidas de la comparación con datos instrumentales de una boya escalar de oleaje. En segunda instancia, presenta una metodología de generación de oleaje por el paso de tormentas tropicales y huracanes en el Caribe colombiano, haciendo uso de datos de velocidad del viento máxima de la tormenta estimados por satélites. Por último, se presentan los regímenes de oleaje, medio y de temporal, en aguas profundas de la misma zona.

The purpose of this work is to ilustrate the use of variational techniques for solving a nonlinea... more The purpose of this work is to ilustrate the use of variational techniques for solving a nonlinear analysis problem. More precisely, we show the existence of at least one solution for a certain sublinear Dirichlet problem when the growth of the nolinearity at infinity is bounded by a line whose slope is less than the first eigenvalue. For proving this theorem we use a classical result of the minimization theory of functionals.

Annali di Matematica Pura ed Applicata, 2011

In this paper, we establish sufficient conditions for an asymptotically linear elliptic boundary ... more In this paper, we establish sufficient conditions for an asymptotically linear elliptic boundary value problem to have at least seven solutions. We use the mountain pass theorem, Lyapunov-Schmidt reduction arguments, existence of solutions that change sign exactly once, and bifurcation properties. No symmetry is assumed on the domain or the non-linearity.

Journal of Mathematical Analysis and Applications, 2013

In this paper we study the existence of multiple solutions for semilinear elliptic boundary value... more In this paper we study the existence of multiple solutions for semilinear elliptic boundary value problems, first when the nonlinearity is asymptotically linear and then when it has an arbitrary behavior for large values of the argument. Our proofs use extensively the global bifurcation theorem and bifurcation from infinity. Additionally, when we can apply the Lyapunov-Schmidt reduction method, we show the existence of multiple solutions, we give an exact number of solutions, and we provide qualitative properties of these solutions.

Complex Variables and Elliptic Equations, 2020

The parqueting-reflection principle is shown to also work for constructing harmonic Green functio... more The parqueting-reflection principle is shown to also work for constructing harmonic Green functions and harmonic Neumann functions for a class of domains, which are bounded by two arcs in C ∞ with a special intersecting angle π/n, n ∈ N *. Applying the Green representation formula and the Neumann representation formula we solve the Dirichlet and Neumann boundary problem to the Poisson equation in these domains.

arXiv: Analysis of PDEs, 2018

In this paper we study the quasilinear equation −ep2Deltau−Deltapu=f(u)- \ep^2 \Delta u-\Delta_p u=f(u)−ep2Deltau−Deltapu=f(u) in a smooth bo... more In this paper we study the quasilinear equation −ep2Deltau−Deltapu=f(u)- \ep^2 \Delta u-\Delta_p u=f(u)−ep2Deltau−Deltapu=f(u) in a smooth bounded domain Omega\OmegaOmega with Dirichlet boundary condition. For epgeq0\ep \geq 0epgeq0, we review existence of a least energy nodal solution and then present information about the Morse Index of least nodal energy solutions this BVP. In particular we provide Morse Index information for the case ep=0\ep =0ep=0.

Journal of Mathematical Analysis and Applications, 2018

In this paper we study multiplicity and qualitative behavior of solutions for semilinear elliptic... more In this paper we study multiplicity and qualitative behavior of solutions for semilinear elliptic problems with neumann boundary condition and asymptotically linear smooth nonlinearity. We provide sufficient conditions on the number of eigenvalues the derivative of the nonlinearity crosses to guarantee existence of at least five nontrivial solutions. The techniques we use are a combination of minimization, Leray-Schauder degree, Morse Theory and Reduction method a la Castro-Lazer.

Electronic Proceedings in Theoretical Computer Science, 2016

We define a mean-field semantics for S-PALPS, a process calculus for spatially-explicit, individu... more We define a mean-field semantics for S-PALPS, a process calculus for spatially-explicit, individualbased modeling of ecological systems. The new semantics of S-PALPS allows an interpretation of the average behavior of a system as a set of recurrence equations. Recurrence equations are a useful approximation when dealing with a large number of individuals, as it is the case in epidemiological studies. As a case study, we compute a set of recurrence equations capturing the dynamics of an individual-based model of the transmission of dengue in Bello (Antioquia), Colombia.

Informador Técnico, 2012

El presente artículo, producto de un proyecto de investigación,1 muestra los resultados de la eva... more El presente artículo, producto de un proyecto de investigación,1 muestra los resultados de la evaluación de la influencia del tiempo transcurrido entre la cosecha y la aplicación de una cera natural en el deterioro de raíces de yuca. Dicho tiempo se denominó “momento de aplicación”. En el desarrollo de este trabajo se utilizó la cera TAO FRESH ROOT de la empresa Tao Química Ltda. Para la evaluación se consideraron tres factores de calidad de las raíces de yuca: deterioro fisiológico, pérdida de peso y contenido de materia seca. Se evaluaron en dos variedades de yuca cinco momentos de aplicación (1, 3, 6, 12 y 24 h) durante un período de 21 días. Presentó los menores promedios de deterioro fisiológico y pérdida de peso el momento de aplicación de 6 h. El prpósito de este artículo es establecer el potencial de las ceras naturales como técnica de conservación de las raíces de yuca y en él se destaca el momento de aplicación como un factor influyente en la prolongación de la vida útil d...

Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2014

In this work we deal with the existence and qualitative properties of the solutions to a supercri... more In this work we deal with the existence and qualitative properties of the solutions to a supercritical problem involving the −∆p(•) operator and the Hardy-Leray potential. Assuming 0 ∈ Ω, we study the regularizing effect due to the addition of a first order nonlinear term, which provides the existence of solutions with a breaking of resonance. Once we have proved the existence of a solution, we study the qualitative properties of the solutions such as regularity, monotonicity and symmetry.

Boletín Científico CIOH, 2005

Resumen-El presente artículo presenta, en primera instancia, las ecuaciones de corrección de los ... more Resumen-El presente artículo presenta, en primera instancia, las ecuaciones de corrección de los datos de oleaje visual proporcionados por los barcos en ruta obtenidas de la comparación con datos instrumentales de una boya escalar de oleaje. En segunda instancia, presenta una metodología de generación de oleaje por el paso de tormentas tropicales y huracanes en el Caribe colombiano, haciendo uso de datos de velocidad del viento máxima de la tormenta estimados por satélites. Por último, se presentan los regímenes de oleaje, medio y de temporal, en aguas profundas de la misma zona.

The purpose of this work is to ilustrate the use of variational techniques for solving a nonlinea... more The purpose of this work is to ilustrate the use of variational techniques for solving a nonlinear analysis problem. More precisely, we show the existence of at least one solution for a certain sublinear Dirichlet problem when the growth of the nolinearity at infinity is bounded by a line whose slope is less than the first eigenvalue. For proving this theorem we use a classical result of the minimization theory of functionals.

Annali di Matematica Pura ed Applicata, 2011

In this paper, we establish sufficient conditions for an asymptotically linear elliptic boundary ... more In this paper, we establish sufficient conditions for an asymptotically linear elliptic boundary value problem to have at least seven solutions. We use the mountain pass theorem, Lyapunov-Schmidt reduction arguments, existence of solutions that change sign exactly once, and bifurcation properties. No symmetry is assumed on the domain or the non-linearity.

Journal of Mathematical Analysis and Applications, 2013

In this paper we study the existence of multiple solutions for semilinear elliptic boundary value... more In this paper we study the existence of multiple solutions for semilinear elliptic boundary value problems, first when the nonlinearity is asymptotically linear and then when it has an arbitrary behavior for large values of the argument. Our proofs use extensively the global bifurcation theorem and bifurcation from infinity. Additionally, when we can apply the Lyapunov-Schmidt reduction method, we show the existence of multiple solutions, we give an exact number of solutions, and we provide qualitative properties of these solutions.

Complex Variables and Elliptic Equations, 2020

The parqueting-reflection principle is shown to also work for constructing harmonic Green functio... more The parqueting-reflection principle is shown to also work for constructing harmonic Green functions and harmonic Neumann functions for a class of domains, which are bounded by two arcs in C ∞ with a special intersecting angle π/n, n ∈ N *. Applying the Green representation formula and the Neumann representation formula we solve the Dirichlet and Neumann boundary problem to the Poisson equation in these domains.

arXiv: Analysis of PDEs, 2018

In this paper we study the quasilinear equation −ep2Deltau−Deltapu=f(u)- \ep^2 \Delta u-\Delta_p u=f(u)−ep2Deltau−Deltapu=f(u) in a smooth bo... more In this paper we study the quasilinear equation −ep2Deltau−Deltapu=f(u)- \ep^2 \Delta u-\Delta_p u=f(u)−ep2Deltau−Deltapu=f(u) in a smooth bounded domain Omega\OmegaOmega with Dirichlet boundary condition. For epgeq0\ep \geq 0epgeq0, we review existence of a least energy nodal solution and then present information about the Morse Index of least nodal energy solutions this BVP. In particular we provide Morse Index information for the case ep=0\ep =0ep=0.

Journal of Mathematical Analysis and Applications, 2018

In this paper we study multiplicity and qualitative behavior of solutions for semilinear elliptic... more In this paper we study multiplicity and qualitative behavior of solutions for semilinear elliptic problems with neumann boundary condition and asymptotically linear smooth nonlinearity. We provide sufficient conditions on the number of eigenvalues the derivative of the nonlinearity crosses to guarantee existence of at least five nontrivial solutions. The techniques we use are a combination of minimization, Leray-Schauder degree, Morse Theory and Reduction method a la Castro-Lazer.

Electronic Proceedings in Theoretical Computer Science, 2016

We define a mean-field semantics for S-PALPS, a process calculus for spatially-explicit, individu... more We define a mean-field semantics for S-PALPS, a process calculus for spatially-explicit, individualbased modeling of ecological systems. The new semantics of S-PALPS allows an interpretation of the average behavior of a system as a set of recurrence equations. Recurrence equations are a useful approximation when dealing with a large number of individuals, as it is the case in epidemiological studies. As a case study, we compute a set of recurrence equations capturing the dynamics of an individual-based model of the transmission of dengue in Bello (Antioquia), Colombia.

Informador Técnico, 2012

El presente artículo, producto de un proyecto de investigación,1 muestra los resultados de la eva... more El presente artículo, producto de un proyecto de investigación,1 muestra los resultados de la evaluación de la influencia del tiempo transcurrido entre la cosecha y la aplicación de una cera natural en el deterioro de raíces de yuca. Dicho tiempo se denominó “momento de aplicación”. En el desarrollo de este trabajo se utilizó la cera TAO FRESH ROOT de la empresa Tao Química Ltda. Para la evaluación se consideraron tres factores de calidad de las raíces de yuca: deterioro fisiológico, pérdida de peso y contenido de materia seca. Se evaluaron en dos variedades de yuca cinco momentos de aplicación (1, 3, 6, 12 y 24 h) durante un período de 21 días. Presentó los menores promedios de deterioro fisiológico y pérdida de peso el momento de aplicación de 6 h. El prpósito de este artículo es establecer el potencial de las ceras naturales como técnica de conservación de las raíces de yuca y en él se destaca el momento de aplicación como un factor influyente en la prolongación de la vida útil d...

Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2014

In this work we deal with the existence and qualitative properties of the solutions to a supercri... more In this work we deal with the existence and qualitative properties of the solutions to a supercritical problem involving the −∆p(•) operator and the Hardy-Leray potential. Assuming 0 ∈ Ω, we study the regularizing effect due to the addition of a first order nonlinear term, which provides the existence of solutions with a breaking of resonance. Once we have proved the existence of a solution, we study the qualitative properties of the solutions such as regularity, monotonicity and symmetry.