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Existence of solutions for a generalized Yang–Mills–Higgs theory

In this paper, the monopoles which are topological solitons in three space dimensions of k-field theories is studied. It is explicitly constructed that the magnetic monopoles arising in the recent study of Casana, Ferreira, and Hora of a generalized Yang–Mills–Higgs model which is controlled by the special positive function f. Using a variational method, we prove the existence of the finite-energy monopoles solution in the non-Abelian gauge field is proven. In particular, it is shown that, under the condition of the special weight function f, the finite-energy solution must be Bogomolnyi–Prasad–Sommerfield solution.