Differential Equations / Ecuaciones Diferenciales

M. Arias, J. Campos, R. Ortega,
L.A. Sánchez, P.J. Torres, A.J. Ureña

Departamento de Matemática Aplicada
Facultad de Ciencias
Campus de Fuentenueva
Universidad de Granada
18071 Granada (Spain)

Updated: February 7,  2012

Members:

Ph D students:  Alexander Gutiérrez alexguti@utp.edu.co , Stefano Marò stefano.maro@unito.it , Andrés Rivera amrivera@puj.edu.co , Alfonso Ruiz-Herrera alfonsoruiz@ugr.es , Manuel Zamora mzc0708@ugr.es

Preprints:

• C. Bereanu, P. Jebelean, P.J. Torres, Positive radial solutions for Dirichlet problems with mean curvature operators in Minkowski space (February 2, 2012), pdf-file

• A. Fonda, R. Toader, P.J. Torres, Periodic motions in a gravitational central field with a rotating external force (December 21, 2011), pdf-file

• A. Gutiérrez, P.J. Torres, Non-autonomous saddle-node bifurcation in a canonical electrostatic MEMS (November 9, 2011), pdf-file

• E. Liz, A. Ruiz-Herrera, The hydra effect, bubbles, and chaos in a simple discrete population model with constant effort harvesting, to appear in Journal of Mathematical Biology (November 2, 2011), pdf-file

• A. Ruiz-Herrera, Chaos in Delay Differential Equations with Applications in Population Dynamics, to appear in Discrete and Continuous Dynamical Systems, Series A (October 19, 2011), pdf-file

• S. Marò, Periodic Solutions of a Forced Relativistic Pendulum via Twist Dynamics (October 4, 2011), pdf-file

• M. Kunze, R. Ortega, Long-time stability estimates for the non-periodic Littlewood boundedness problem (September 29, 2011), pdf-file

• M. Kunze, R. Ortega, Twist mappings with non-periodic angles, CIME course "Stability and Bifurcation for non-autonomous differential equations", Cetraro, June 2011 (September 22, 2011), pdf-file

• A. Ruiz-Herrera, Topological Criteria of Global Attraction with Applications in Population Dynamics (September 9, 2011), pdf-file

• A. Margheri, R. Ortega, C. Rebelo, Some analytical results about periodic orbits in the restricted three body problem with dissipation (August 21, 2011) pdf-file

• R. Hakl, P.J. Torres, M. Zamora, Periodic solutions of singular second order differential equations: the repulsive cases (February 21, 2011) pdf-file

• J. Campos, P. Guerrero, O. Sánchez, J. Soler, On the analysis of travelling waves to a nonlinear flux limited reaction-diffusion equation , to appear in Annales de l'Institut Henri Poincaré Analyse Non Linéaire (February 21, 2011) pdf-file

• M. Arias, J. Campos, Jugando con matrices positivas: eficiencia de un estado inicial (February 21, 2011) pdf-file

• A.J. Ureña, Instability of periodic minimizers in finite dimensions (January 16, 2011) pdf-file

• C. Bereanu, P.J. Torres, Existence of at least two periodic solutions of the forced relativistic pendulum to appear in Proc. Am. Math. Soc. (December 16, 2010) pdf-file

• D. Bonheure, P.J. Torres, Bounded and homoclinic like solutions of a second order singular differential equation to appear in Bull. London Math. Soc. (December 16, 2010) pdf-file

• A. Ruiz-Herrera, F. Zanolin, An example of chaotic dynamics in 3D systems via stretching along paths (November 30, 2010) pdf-file

• L.A. Sánchez, One-dimensional compact invariant sets for scalar periodic reaction-diffusion equations on the circle (September 30, 2010) pdf-file

• L. Hernández-Corbato, R. Ortega, F. R. Ruiz del Portal, Attractors with irrational rotation number to appear in Math. Proc. Camb. Phil. Soc. (September 12, 2010) pdf-file

• A. Ruiz-Herrera, Exclusion and dominance in discrete population models via the Carrying Simplex (June 10, 2010), to appear in Journal of Difference Equations and Applications pdf-file

• J.A. Cid, P.J. Torres, On the existence and stability of periodic solutions for pendulum-like equations with friction and $\phi$-Laplacian (November 1, 2009) pdf-file

• R. Ortega, Topology of the plane and periodic differential equations (work in progress) (July 1, 2008) Chapter 1. pdf-file  Chapter 2.pdf-file Chapter 3. pdf-file Chapter 5.pdf-file

Publications:  

      2012

•  A. Buica, R. Ortega, Persistence of equilibria as periodic solutions of forced systems, Journal of Differential Equations 252 (2012) 2210-2221 pdf-file

• J. Chu, N. Fan, P.J. Torres, Periodic solutions for second order singular damped differential equations, Journal of Mathematical Analysis and applications 388 (2012) 665-675 pdf-file

• A. Gutiérrez, P.J. Torres, The Lazer-Solimini equation with state-dependent delay, Applied Mathematics Letters 25 (2012) 643-647pdf-file

• A. Ruiz-Herrera, Chaos in Predator Prey Systems With/Without Migration, Nonlinear Analysis: Real World and Applications 13 (2012) 977-986 pdf-file

     2011

• N. Alkoumi, The number of periodic solutions of some analytic equations of Abel type, Nonlinear Analysis: Theory, Methods & Applications 74 (2011) 5352-5358 pdf-file

• N. Alkoumi, P. J. Torres, On the number of limit cycles of a generalized Abel equation, Czechoslovak Mathematical Journal 61 (2011) 73-83 pdf-file    

•  N. Alkoumi, P.J. Torres, Estimates on the number of limit cycles of a generalized Abel equation, Discrete and Continuous Dynamical Systems 31 (2011) 25-34. pdf-file

• P. Amster, J. Haddad, R. Ortega, A. J. Ureña, Periodic motions in forced problems of Kepler type, Nonlinear Differential Equations and Applications 18 (2011) 649-657 pdf-file

• M. Arias, J. Campos, L. Sanchez, A. Robles-Pérez, Erratum to: Fast and heteroclinic solutions for a second order ODE related to Fisher-Kolmogorov’s equation, Calc. Var. 40 (2011) 291–292 pdf-file   

• C. Escudero, A. Rivera, P. Torres, Chemical Oscillations out of Chemical Noise, SIAM J. Appl. Dyn. Syst. 10 (2011) 960-986 pdf-file

•  A. Fonda, A. J. Ureña, Periodic, subharmonic, and quasi-periodic oscillations under the action of a central force, Discrete and Continuous Dynamical Systems, 29 (2011) 169-192 pdf-file   

• A. Gutiérrez, P.J. Torres, Periodic solutions of Liénard second order differential equations with one or two weak singularities, Differential Equations & Applications- DEA 3 (2011) 375-384 pdf-file

• R. Hakl, P.J. Torres, A combined variational-topological approach for dispersion-managed solitons in optical fibers, Z. Angew. Math. Phys. 62 (2011) 245–266. pdf-file

• R. Halk, P.J. Torres, Maximum and antimaximum principles for a second order differential operator with variable coefficients of indefinite sign, Applied Mathematics and Computation 217 (2011) 7599-7611.pdf-file

• R. Hakl, P.J. Torres, M. Zamora, Periodic solutions of singular second order differential equations: upper and lower functions, Nonlinear Analysis: Theory, Methods & Applications 74 (2011) 7078-7093 pdf-file

• M. Kunze, R. Ortega, Complete orbits for twist maps on the plane: extensions and applications, Journal of Dynamics and Differential Equations 23 (2011) 405-423 pdf-file

• M. Kunze, R. Ortega, Complete orbits for twist maps on the plane: the case of small twist, Ergodic Theory and Dynamical Systems 31 (2011) 1471-1498 pdf-file

• O. Makarenkov, R. Ortega, Asymptotic stability of forced oscillations emanating from a limit cycle, Journal of Differential Equations 250 (2011) 39-52 pdf-file

• S. Middelkamp, P.J. Torres, P.G. Kevrekidis, R. Carretero-González, P. Schmelcher, D.V. Freilich, D.S. Hall, Guiding-center dynamics of vortex dipoles in Bose-Einstein condensates, Phys. Rev. A 84 (2011) 011605(R) pdf-file

• R. Ortega, Linear motions in a periodically forced Kepler problem, Portugaliae Mathematica 68 (2011) 149-176 pdf-file

• R. Ortega, A dynamical characterization of planar symmetries, Qualitative Theory of Dynamical Systems 10 (2011) 197-201 pdf-file

• R. Ortega, A difference equation arising in Mechanics, Proceedings of the International Workshop Future Directions in Difference Equations. June 13-17, 2011, Vigo, Spain, pages 145-148.pdf-file

• R. Ortega, F.R. Ruiz del Portal, Attractors with vanishing rotation number, Journal European Math. Soc. 13 (2011) 1567–1588 pdf-file

• A. Ruiz-Herrera, Permanence of two species and fixed point index, Nonlinear Analysis 74 (2011) 146-153 pdf-file

• A. Ruiz-Herrera, Location of fixed points in the presence of two cycles, Topological Methods in Nonlinear Analysis 38 (2011) 407-420 pdf-file

• P.J. Torres, Stabilization of optically coupled lasers with periodic pumping, Nonlinear Oscillations 14 (2011) 392-399 pdf-file

• P. J. Torres, Nondegeneracy of the periodically forced Liénard differential equation with $\phi$-Laplacian, Communications in Contemporary Mathematics 13 (2011) 283-292. pdf-file

• P.J. Torres, R. Carretero-González, S. Middelkamp, P. Schmelcher, D.J. Frantzeskakis and P.G. Kevrekidis, Vortex Interaction Dynamics in Trapped Bose-Einstein Condensates, Communications on Pure and Applied Analysis 10 (2011) 1589-1615 pdf-file

• P.J. Torres, P.G. Kevrekidis, D.J. Frantzeskakis, R. Carretero-González, P. Schmelcher and D.S. Hall, Dynamics of vortex dipoles in confined Bose–Einstein condensates, Physics Letters A 375 (2011) 3044-3050 pdf-file  

• A. J. Ureña, Dynamics of periodic second-order equations between an ordered pair of lower and upper solutions, Advanced Nonlinear Studies 11 (2011) 675-694 pdf-file

2010

• M. Arias, M. Cuesta, A one side superlinear Ambrosetti-Prodi problem for the Dirichlet p-Laplacian, Journal of Mathematical Analysis and Applications 367 (2010), 499-507 pdf-file

• J.L. Bravo, P.J. Torres, Periodic solutions of a singular equation with indefinite weight, Advanced Nonlinear Studies 10 (2010), 927-938 pdf-file

• R. Halk, P.J. Torres, On periodic solutions of second-order differential equations with attractive-repulsive singularities, Journal of Differential Equations, 248  (2010)  111-126. pdf-file

• R. Ortega, A. Rivera, Global bifurcations from the center of mass in the Sitnikov problem, Discrete and Continuous Dynamical Systems B 14 (2010) 719-732 pdf-file

• A. Ruiz-Herrera, Coexistence states for cyclic 3-dimensional systems, Advanced Nonlinear Studies, 10 (2010) 401-412.  pdf-file

• L.A. Sánchez, Convex cones associated to generalized cones in R^n , Linear Algebra and its Applications, 433 (2010) 2122-2138.pdf-file

• L.A. Sánchez, Existence of periodic orbits for high-dimensional autonomous systems, Journal of Mathematical Analysis and Applications, 363 (2010) 409-418. pdf-file

• A. J. Ureña, Invariant manifolds around equilibria of Newtonian equations: some pathological examples, Journal of Differential Equations 249 (2010) 366-391 pdf-file

             1994 - 2009

Editorial work:

• R. Ortega: Advanced Nonlinear Studies,   Archiv der Mathematik,   Mediterranean Journal of Mathematics, Nonlinear Analysis TMA ,  Nonlinear Differential Equations and Applications NoDEA,  Portugaliae Mathematica, Studia Universitatis Babes-Bolyai Mathematica ,  ZAMP.

Visitors and conferences:

2011/2012

• October 16-23, Petru Jebelean, West University of Timisoara, " Multiple critical orbits for a class of lower semicontinuous functionals"

• September 1-November 30, Alessandro Fonda, Università di Trieste, "A general method for the existence of periodic solutions of differential systems in the plane"

• September 1-November 30, Rodica Toader, Università di Udine, "Periodic solutions of pendulum-like Hamiltonian systems in the plane"

• September 1 -February 28, Cristian Bereanu, Institute of Mathematics “Simion Stoilow”, Romanian Academy "Multiple solutions for periodic problems with singular phi-Laplacian", "Positive radial solutions for Dirichlet problems with mean curvature operators in Minkowski space"

2010/2011

• August 29-30, Vladimir Konotop, Universidade de Lisboa

• May 16-21, Markus Kunze, Universität Duisburg-Essen

• April 26-29, May 23-27, Rogério Martins, Universidade Nova de Lisboa

• February 14-22, Carlota Rebelo, Universidad de Lisboa

• February 14-22, Alessandro Margheri, Universidad de Lisboa

• January 1-31, Begoña Alarcón, Universidad de Oporto, "Aplicaciones equivariantes del plano"

• January 17-21, Ricardo Enguiça, ISEL Lisboa, "Heteroclinics for some equations involving the P-laplacian operator"

• November 22-26, Cristian Bereanu, "Simion Stoilow" Institute of Mathematics of the Romanian Academy, "Szulkin critical point theory for nonlinear perturbations of singular phi-Laplacians"

• October 26-28, Jaime Sánchez Gabites, Universidad de Castilla-La Mancha, "Más allá de la no celularidad: una curiosa propiedad de la bola de Alexander y sus consecuencias dinámicas"

• October 20-22, Armengol Gasull, Universitat Autonoma de Barcelona, "Dinámica de las ecuaciones periódicas de Lyness

         1996/1997 - 2009/2010

Ph. Dissertations:

• Naeem Alkouimi, The number of limit cycles of a generalized Abel equation, Universidad de Granada,  October 2010. pdf-file

• María José Romero Vallés, Propiedades dinámicas de un modelo con impactos: caída de granos sobre un perfil escalonado, Universidad de Granada,  November 2008. pdf-file

• Rogério Martins, Dinâmica de sistemas dissipativos e não-autónomos com uma coordenada angular, Universidade de Lisboa, 2005. pdf-file

• Antonio J. Ureña, Nonlinear boundary value problems, Universidad de Granada, November 2002. pdf-file

• Daniel Núñez, Estabilidad de oscilaciones periódicas en una ecuación de Newton no autónoma, Universidad de Granada, November 2001. pdf-file

• Aureliano M. Robles-Pérez, Las soluciones periódicas de una ecuación de la cuerda vibrante, Universidad de Granada, September 2000. pdf-file

• Luis Ángel Sánchez, Sistemas monótonos, grado topológico y estabilidad orbital en tres dimensiones, Universidad de Granada, July 2000. (No ps-file available, the author will send a copy if requested)

• Pedro J. Torres, Estudio cualitativo de ecuaciones diferenciales con término no lineal singular, Universidad de Granada, March 1998. ps-file

• Juan Campos, Espectro de Fucík para operadores elípticos, Universidad de Granada, July 1996. (No ps-file available, the author will send a copy if requested)

• Rafael Ortega, Estudio cualitativo del rango de operadores diferenciales elípticos semilineales, Universidad de Granada, December 1984. (No ps-file available, the author will send a copy if requested)

More information:

teaching

• Rafael Ortega www

and more...

• Homenaje a Jean Mawhin. Sevilla, abril 2003 www
• Recent Trends on Nonlinear Science 2007 in Granada www
• Interdisciplinary Workshop on Periodic Oscillations, Granada October 20-23, 2009  schedule    abstracts
• Interdisciplinary Workshop on Quantum Mechanics and Dynamical Systems, Granada October 8-10, 2011  schedule
• DANCE NET (Dinámica, Atractores y Nolinealidad: Caos y Estabilidad) www

Updated: February 7, 2012