UGR

Pedro José Torres Villarroya (Coordinator)

Juan Campos Rodríguez

Rafael Ortega Ríos

Antonio Jesús Ureña Alcázar

Universidad de Granada

The Group of Differential Equations at University of Granada has a nearly 30-year experience in qualitative analysis of differential equations. Our work philosophy can be summarized in the study of differential equations of interest in any scientific discipline by combining imaginative as possible of general mathematical tools and methods from different sources. Generally, the studied systems are not autonomous, ie have an explicit dependence of time, and the results sought are global or non-perturbative, ie not assumed that the parameters describing the system are small.
Today our goals are described in the following research lines:

- Nonlinear oscillators:
- Periodic solutions in systems with singularities.
- Stability criteria. Stabilization of equilibria.
- Global Methods on Celestial Mechanics.
- Location of quantitative solutions.
- Evolution equations:
- Nonlinear Schrödinger equation as a dynamical system. Applications to Bose-Einstein condensates and nonlinear optics.
- Navier-Stokes Equations: Existence of limit cycles and stability.
- Wave Equations: Interconnection between the highest principles and properties of monotony.
- Mathematical aspects of biology:
- Exclusion principle in competitive systems.
- Biological synchronization.
- Traveling waves in reaction-diffusion equations. Application to models of pattern formation and tumor growth.

Juan Campos Rodríguez

Rafael Ortega Ríos

Antonio Jesús Ureña Alcázar