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: May 15, 2013
Members:
Ph D students: Daniel de la Fuente
danieldf862@hotmail.com, Stefano Marò
stefano.maro@unito.it , Alfonso Ruiz-Herrera
alfonsoruiz@ugr.es , Manuel Zamora
mzamora@ugr.es
Preprints:
- R. Ortega, Stable periodic solutions in the forced pendulum equation (May 15, 2013) pdf-file
- S. Marò, Relativistic pendulum and invariant curves (May 3, 2013) pdf-file
- P.J. Torres,
P. Madhusudhanan, L. W. Esposito, Mathematical analysis of a model for moon-triggered clumping in Saturn's rings (February 22, 2013) pdf-file
- A. Boscaggin, P.J. Torres, Periodic motions of fluid particles induced by a prescribed vortex path in a circular domain (February 13, 2013) pdf-file
- C. Escudero, R. Hakl, I. Peral, P.J. Torres,
Existence and nonexistence results for a singular boundary value problem arising in the theory of epitaxial growth (December 25, 2012) pdf-file
- R. Ortega, Translation arcs and stability in two dimensions (November 8, 2012) pdf-file
- J.L. López, E. Pérez Sinusía, P.J. Torres, One dimensional boundary value problems, Green functions and the contraction principle (May 28, 2012) , pdf-file
- C. Bereanu, P. Jebelean, P.J. Torres, Multiple positive radial solutions for a Dirichlet problem involving the mean curvature operator in Minkowski space (May 28, 2012), pdf-file
- A. Gutiérrez, P.J. Torres, Non-autonomous saddle-node bifurcation in a canonical electrostatic MEMS (November 9, 2011), pdf-file
- S. Marò, Periodic Solutions of a Forced Relativistic Pendulum via Twist Dynamics, to appear in Topological Methods in Nonlinear Analysis (October 4, 2011), pdf-file
- M. Kunze, R. Ortega, Long-time stability estimates for the non-periodic Littlewood boundedness problem, to appear in Proc. London Math. Soc. (Sept. 29, 2011. New version April 23, 2012), pdf-file
- A. Ruiz-Herrera, F. Zanolin, An example of chaotic dynamics in 3D systems via stretching along paths to appear in Annali di Matematica Pura ed Applicata (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
Publications:
2013
- C. Bereanu, P. Jebelean, P.J. Torres, Positive radial solutions for Dirichlet problems with mean curvature operators in Minkowski space, Journal of Functional Analysis 264 (2013) 270-287 pdf-file
- J. Campos, P. Guerrero, O. Sánchez, J. Soler, On the analysis of travelling waves to a nonlinear flux limited reaction-diffusion equation, Annales de l'Institut Henri Poincaré Analyse Non Linéaire
30 (2013) 141-155 pdf-file
- J. Campos, M. Tarallo, Nonmonotone equations with large almost periodic forcing terms, Journal of Differential Equations 254 (2013) 686-724 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, Discrete and Continuous Dynamical Systems 33 (2013) 141-153 pdf-file
- C. Escudero, R. Hakl, I. Peral, P.J. Torres, On the radial stationary solutions to a model of nonequilibrium growth, European Journal of Applied Mathematics 24 (2013) 437-453 pdf-file
- Q.D. Katatbeh, P.J. Torres, Existence of periodic and solitary waves for a Nonlinear Schrödinger Equation with Nonlocal Integral Term of convolution type , Communications in Nonlinear Science and Numerical Simulation 18 (2013) 1136–1142 pdf-file
- M. Kunze, R. Ortega, Twist mappings with non-periodic angles, Stability and bifurcation theory for non-autonomous differential equations, Lecture Notes in Mathematics, Springer, 2013, 267–302 pdf-file
- S. Marò, Coexistence of bounded and unbounded motions in a bouncing ball model, Nonlinearity 26 (2013) 1439-1448 pdf-file
- R. Ortega, Prevalence of non-degenerate periodic solutions in the forced pendulum equation, Advanced Nonlinear Studies 13 (2013) 219-229 pdf-file
- A. Ruiz-Herrera, Chaos in Delay Differential Equations with Applications in Population Dynamics, Discrete and Continuous Dynamical Systems 33 (2013) 1633-1644
- A. Ruiz-Herrera, Exclusion and dominance in discrete population models via the Carrying Simplex, Journal of Difference Equations and Applications
19 (2013) 96-113 pdf-file
- A. Ruiz-Herrera, P.J. Torres, Periodic solutions and chaotic dynamics in forced impact oscillators, SIAM J Applied Dynamical Systems
12 (2013) 383-414 pdf-file
- P.J. Torres, A.J. Ureña, M. Zamora, Periodic and quasi-periodic motions of a relativistic particle under a central force field, Bulletin of the London Mathematical Society 45 (2013) 140-152 pdf-file
- P.J. Torres,
Z. Cheng, J. Ren,
Non-degeneracy and Uniqueness of Periodic Solutions for 2n-order Differential Equations
, Discrete and Continuous Dynamical Systems A
33 (2013)
2155 - 2168 pdf-file
- A.J. Ureña, Instability of periodic minimizers in finite dimensions, Discrete and Continuous Dynamical Systems 33 (2013) 345-357 pdf-file
2012
- C. Bereanu, P.J. Torres, Existence of at least two periodic solutions of the forced relativistic pendulum, Proc. Am. Math. Soc. 140 (2012) 2713-2719 pdf-file
- D. Bonheure, P.J. Torres, Bounded and homoclinic like solutions of a second order singular differential equation, Bulletin London Math. Soc 44 (2012) 47-54 .pdf-file
- 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. Fonda, R. Toader, P.J. Torres, Periodic motions in a gravitational central field with a rotating external force, Celestial Mechanics and Dynamical Astronomy, 113 (2012)
335-342 pdf-file
- A. Gutiérrez, P.J. Torres, The Lazer-Solimini equation with state-dependent delay, Applied Mathematics Letters 25 (2012) 643-647 pdf-file
- R. Hakl, P.J. Torres, M. Zamora, Periodic solutions of singular second order differential equations: the repulsive cases,Topological Methods in Nonlinear Analysis 39 (2012) 199-220 pdf-file
- L. Hernández-Corbato, R. Ortega, F. R. Ruiz del Portal, Attractors with irrational rotation number, Math. Proc. Camb. Phil. Soc. 153 (2012) 59–77 pdf-file
- E. Liz, A. Ruiz-Herrera, Chaos in discrete structured population models, SIAM J. Applied Dynamical Systems
11 (2012) 1200-1214 pdf-file
- E. Liz, A. Ruiz-Herrera, The hydra effect, bubbles, and chaos in a simple discrete population model with constant effort harvesting, Journal of Mathematical Biology 65 (2012) 997-1016, pdf-file
- A. Margheri, R. Ortega, C. Rebelo, Some analytical results about periodic orbits in the restricted three body problem with dissipation, Celestial Mechanics and Dynamical Astronomy 113 (2012) 279-290 pdf-file
- R. Ortega, The complex periodic problem for a Riccati equation, Annals of the University of Bucharest (mathematical series) 3 (LXI) (2012), 219-226 pdf-file
- R. Ortega, A. Ruiz-Herrera, Index and persistence of stable Cantor sets, Rendiconti dell'Istituto di Matematica dell'Università di Trieste 44 (2012) 33-34, pdf-file
- A. Ruiz-Herrera, Chaos in Predator Prey Systems With/Without Migration, Nonlinear Analysis: Real World and Applications 13 (2012) 977-986 pdf-file
- A. Ruiz-Herrera, Topological Criteria of Global Attraction with Applications in Population Dynamics, Nonlinearity
25 (2012) 2823-2841 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, Jugando con matrices positivas: eficiencia de un estado inicial, Florentino García Santos: In Memoriam. Editorial Universidad de Granada. Granada, 2011, pp.: 15-22 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. Halk, 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. Schemelcher, D.J. Frantzeskakis, 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. Schemelcher, 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
1994 - 2009
Editorial work:
Visitors and conferences:
2012/2013
- April 5-12, Grzegorz Graff, Gdansk University of Technology, "Fixed point indices of iterated maps and their applications"
- April 4-12, Luis Franco, UAM México, "Dinámica en el Problema Restringido de 3 Cuerpos en el círculo unitario"
- March 20, Abimael Bengochea, UNAM México, "Órbitas periódicas de tipo herradura en el problema gravitacional de 5 cuerpos"
- March 4-12, Carlota Rebelo, Universidad de Lisboa
- March 4-12, Alessandro Margheri, Universidad de Lisboa
- February 25-27, Daniel Peralta Salas, ICMAT Madrid, "Movimiento de cargas en campos magnéticos: resultados, aplicaciones y problemas abiertos"
- February 18-22, Alessandro Fonda, Università degli Studi di Trieste, "Generalized Sturm-Liouville boundary conditions for first order differential systems in the plane"
- December 10-21,
Hafidha Sebbagh, University Abou-Bekr Belkaid (Tlemcen), "Exact number of positive solutions for a class of quasilinear boundary value problems with a singular nonlinearity"
- November 26-30, Markus Kunze, Universität Köln
- November 12-December 8,
Alberto Boscaggin,
SISSA (Trieste), "Pairs of solutions to super-sublinear boundary value problems"
- October 1,
Víctor Pérez García, Universidad de Castilla-La Mancha, "Nuevas terapias contra tumores cerebrales basadas en modelos matemáticos"
- September 3-12, Jaime Sánchez Gabites, Universidad de Castilla-La Mancha,
"Bloques aislantes regulares para flujos en 3-variedades"
2011/2012
- May 11-18, Alessandro Margheri, Universidad de Lisboa
- May 11-18, Carlota Rebelo, Universidad de Lisboa
- May 8-17, Massimo Tarallo, Università degli studi di Milano,
"Nonmonotone equations with large almost periodic forcing terms"
- May 7-11, Jesús Palacián, Universidad Pública de Navarra,
"El Estado de Transición en Mecánica Celeste y Dinámica Molecular Desde una Perspectiva Geométrica"
- May 7-11, Patricia Yanguas, Universidad Pública de Navarra
- April 17-27, Arturo de Pablo, Universidad Carlos III, "Nonlinear nonlocal diffusion: Fractional porous medium equation"
- April 16-27, Rogério Martins, Universidade Nova de Lisboa
- March 17-31, Robert Hakl, University of Brno, "Topological methods for the study of differential equations with singularities"
- February 13-18, Carlos Escudero, Universidad Autónoma de Madrid, "Teoría cinética de la coagulación de dos especies"
- 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"
1996/1997 - 2010/2011
Ph. Dissertations
- Alexánder Gutiérrez, Existencia y estabilidad de soluciones periódicas en ecuaciones con singularidades, Universidad de Granada, June 2012. pdf-file
- Andrés M. Rivera, Bifurcación de soluciones periódicas en el problema de Sitnikov, Universidad de Granada, May 2012. pdf-file
- 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
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: May 15, 2013
