Variational methods in the study of nonlinear problems and applications

In this paper we illustrate the lineguides of our research group. We describe some recent results concerning the study of some nonlinear differential equations and systems having a variational nature and arising from physics, geometry and applied sciences. In particular we report existence, multiplicity and regularity results for the solutions of these nonlinear problems. We point out that, in treating the above problems, the used methods for finding solutions are variational and topological, indeed the existence of solutions of the considered equations is obtained searching for critical points of suitable functionals defined on manifolds embedded into infinite dimensional functional spaces, while the regularity of the solutions is studied by means of geometric and harmonic analysis tools.