Remarks on quasilinear elliptic equations as models for elementary particles (Q1422527)

The authors deal with the existence of solitary waves of finite energy and consider equation \[ -\Delta_p u+ F'(u)= 0\quad\text{in }\mathbb R^N,\tag{1} \] where \(\Delta_p u:= \text{div}(|\nabla u|^{p-2}\nabla u)\) and \(F\) satisfies natural assumptions. First the authors study the scalar equation (1) and establish some nonexistence results, which are new in the case \(p> N\). As for the vector-valued fields the situation is different. The solutions the authors consider are called topological solitary waves (for short topological solutions): not only do they vanish at infinity but they are also characterized by a topological invariant, the charge.