The Lee-Weinberg magnetic monopole of unit charge: Existence and uniqueness

We prove the existence and uniqueness of a spherically symmetric monopole solution in the Abelian model of Lee and Weinberg in the BPS limit. The solution carries finite energy and unit charge and generalizes the classical SU(2) BPS monopole. We also prove an existence theorem for the model with a general Higgs field-dependent mass term and establish the equivalence of the second-order equations of motion and the first-order Bogomol'nyi equations within radial symmetry assumption and BPS limit. Our methods have wide applicability in other monopole problems.