Minimum Action Solutions of Some Vector Field Equations

The system of equations studied in this paper is —Au—gXu) on R, d^2, with w R ^ R " and g(u) = dG/dui. Associated with this system is the action, S(u) = J {i|Fw|G(u)}. Under appropriate conditions on G (which differ for d = 2 and d_-3) it is proved that the system has a solution, wφO, of finite action and that this solution also minimizes the action within the class {v is a solution, v has finite action, ι>φθ}.