Partial differential equations: We study nonlinear elliptic problems by means of variational and topological methods. We use topological degree, Morse index and Lusternik Schnirelmann to obtain results about existence and multiplicity of solutions and their qualitative properties.
Semiclassical limit and concentration phenomena: We consider elliptic equations depending on a parameter, defined on an open set of Rn or on a compact Riemannian manifold. We look for multiplicity result of solutions and we describe the shape of these solutions while the parameter is sufficiently small.
Solitons in nonlinear field equations: The Nonlinear Schroedinger and Nonlinear Klein Gordon equations admit, depending on the nonlinearity, solitary wave solutions that are stable. These solutions are called solitons. We study existence and stabilty of solitary waves and we try to describe the dynamics of a soliton under the effect of an external potential.
