We propose a novel method for calculating resonances in three-body Coulombic systems. The method is based on the solution of the set of Faddeev and Lippmann-Schwinger integral equations, which are designed for solving the three-body Coulomb problem. The resonances of the three-body system are defined as the complex-energy solutions of the homogeneous Faddeev integral equations. We show how the kernels of the integral equations should be continued analytically in order that we get resonances. As a numerical illustration a toy model for the three-$alpha$ system is solved.
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