- Variational Methods
- Perturbative Methods in Critical Point Theory
- Elliptic Equations on R^n and Nonlinear Schroedinger Equation
- H-Surfaces
- Singularly Perturbed Problems
- Geometric PDEs
- Hamiltonian systems
- Chaotic Dynamics and Arnold Diffusion
- KAM Theory
- Periodic Solutions of Infinite Dimensional Systems

Research Group:

## Topological and variational methods in critical point theory

- Degree theory
- Sard's Theorem
- The Brouwer fixed point theorem with applications
- The Schauder fixed-point theorem with applications
- Critical points
- Differential calculus and critical points; constrained critical points
- Minimization problems
- Linear eigenvalues and their variational characterization
- Ekeland's variational principle
- The Palais-Smale condition
- Min-Max methods
- Linking and Mountain-Pass theorems

## Topological Degree and Variational Methods, with Applications to the Problem of Bubbles with Prescribed Mean Curvarture

- Degree theory:
- Topological approach to finite-dimensional problems.
- Sard's Theorem.
- Finite dimensional degree theory and the Brouwer fixed point theorem.
- Topological degree in infinite-dimensional Banach spaces.
- The Schauder fixed-point theorem.
- Application to the H-bubble problem:
- Preliminaries on the H-bubble problem: the mean curvature of a radial graph in Rn over the unit sphere.