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We prove the existence of electrically and magnetically charged particlelikestatic solutions, known as dyons, in the minimally gauged Skyrme modeldeveloped by Brihaye, Hartmann, and Tchrakian. The solutions are sphericallysymmetric, depend on two continuous parameters, and carry unit monopole andmagnetic charges but continuous Skyrme charge and non-quantized electric chargeinduced from the 't Hooft electromagnetism. The problem amounts to obtaining afinite-energy critical point of an indefinite action functional, arising fromthe presence of electricity and the Minkowski spacetime signature. Thedifficulty with the absence of the Higgs field is overcome by achievingsuitable strong convergence and obtaining uniform decay estimates at singularboundary points so that the negative sector of the action functional becomestractable.

Existence of Dyons in Minimally Gauged Skyrme Model via Constrained Minimization