The boundary effects affecting the Hamiltonian for the nanocone with curvature-induced spin-orbit coupling were considered and the corresponding electronic structure was calculated. These boundary effects include the spin-orbit coupling, the electron mass acquisition and the Coulomb interaction. Different numbers of the pentagonal defects in the tip were considered. The matrix and analytical form of the Green function approach was used for the verification of our results and the increase of their precision in the case of the spin-orbit coupling.