Nonlinear Elliptic Systems with Critical Growth

The dissertation delas with existence and nonexistence results for a class of nonlinear elliptic systems which arise in looking for solitary waves in coupling the matter field with the electromagnetic field when the nonlinearity exhibits some critical behaviour; in particular this is the case of solitons which are in equilibrium with their own electromagnetic field. In the second part of the dissertation, the author develop a technique to characterize, in a variational framework, the ground state energy level of a large class of critical Hamiltonian elliptic systems.

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obtained his PhD in pure mathematics in 2006 under the guidance of Prof. Bernhard Ruf. His field of research concerns Partial Differential Equations and applications, in particular: elliptic systems, higher order nonlocal PDE with singular nonlinearities and applications to nanotechnologies, best constants in borderline inequalities.