Abstract

The aim of this Letter is to prove the existence of a static solution to the Lorentz invariant equation square (2)u+epsilon square (6)u+V'(u)=0 in every class of maps with nonzero topological charge when the singular potential 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].