In this paper we study a class of Lorentz invariant nonlinear field equatio
ns in several space dimensions. The main purpose is to obtain soliton-like
solutions. These equations were essentially proposed by C. H. DERRICK in a
celebrated paper in 1964 as a model for elementary particles. However, an e
xistence theory was not developed.
The fields are characterized by a topological invariant, the charge. We pro
ve the existence of a static solution which minimizes the energy among the
configurations with nontrivial charge.
Moreover, under some symmetry assumptions, we prove the existence of infini
tely many solutions, which are constrained minima of the energy. More preci
sely, fur every n is an element of N there exists a solution of charge n.