We prove the existence of electrically and magnetically charged particlelike
static solutions, known as dyons, in the minimally gauged Skyrme model
developed by Brihaye, Hartmann, and Tchrakian. The solutions are spherically
symmetric, depend on two continuous parameters, and carry unit monopole and
magnetic charges but continuous Skyrme charge and non-quantized electric charge
induced from the 't Hooft electromagnetism. The problem amounts to obtaining a
finite-energy critical point of an indefinite action functional, arising from
the presence of electricity and the Minkowski spacetime signature. The
difficulty with the absence of the Higgs field is overcome by achieving
suitable strong convergence and obtaining uniform decay estimates at singular
boundary points so that the negative sector of the action functional becomes
tractable.Comment: 24 page