A note on static solutions of a Lorentz invariant equation in dimension 3

The aim of this Letter is to prove the existence of a static solution to th e Lorentz invariant equation square (2)u+epsilon square (6)u+V'(u)=0 in eve ry class of maps with nonzero topological charge when the singular potentia l V has some radial symmetry. Here u:R3+1-->R-4, u=u(x,t), x is an element ofR(3), t is an element ofR and square (p)u=partial derivative/partial derivativet [(c(2)|delu|(2)-|u(t)|(2 ))(p-2) u(t)]-c(2)del [(c(2)|delu|(2)-|u(t)|(2))(p-2)delu].