Abstract
The question of existence of various forms of spherically symmetric particle-like solutions within the theory of general relativity with nonlinear electromagnetic fields is considered. Such solutions are those with a regular center and those with a throat and second spatial asymptote. It will be shown that in the given class of theories: 1) particle-like solutions with nonzero magnetic charge do not exist, and 2) particle-like solutions do not exist for gauge invariant Lagrangians. For the class of Lagrangians with explicit dependence upon potential, particle-like solutions of both types are obtained and limits of their parameters are determined
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