  We present a model where the lepton masses are the eigenvalues of
relativistic nonlinear field equations. The eigenfunctions correspond in the
model to lepton states with inner structure. In this picture the
self-interaction leads to the bound state of electron described by the ground
state solution. The variational approach based on minimization of the mass or
the energy of the ground state solution is developed. The analytical solution
yields the relation between the coupling constant $G_l$ of the self-interaction
and the electron mass as $m_e\simeq 2.3\sqrt{\hbar c/G_l}$. This solution also
leads to a finite `radius' of the electron which is about $1.9\lambda_e$ where
$\lambda_e$ is the Compton length of electron.
