In an approach of low transparency of the barrier the tunneling of electrons through doubly degenerate local state has been considered with allowance for the Coulomb and electron-phonon interactions. It is shown that in the case of weak electron-phonon and strong electron-electron interactions the dependence of tunneling current on the applied voltage has a step-like character at low temperature. The threshold value of the current was measured for small applied bias. The bistable state of the tunneling current is possible in the region of large bias. In the case of strong electron-phonon and weak electron-electron interactions, the threshold of tunneling current can be bistable. This result is a direct consequence of the electron pairing in local states.

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