Structure of exact solutions modelling confinement is discussed for SU(3)-Yang-Mills equations and uniqueness of such confining solutions is proved in a certain sense. Relationship of the obtained results to QCD and the confinement mechanism is considered. Incidentally the Wilson confinement criterion for the found solutions is verified and also numerical estimates for strength of magnetic colour field responsible for linear confinement are adduced in the ground state of charmonium.

The black hole physics techniques and results are applied to find the set of the exact solutions of the SU(3)-Yang-Mills equations in Minkowski spacetime in the Lorentz gauge. All the solutions contain only the Coulomb-like or linear in r components of SU(3)-connection. This allows one to obtain some possible exact and approximate solutions of the corresponding Dirac equation that can describe the relativistic bound states. Possible application to the relativistic models of mesons is also outlined.

The recently obtained solutions of the Dirac equation in the confining SU(3)-Yang-Mills field in Minkowski spacetime are applied to describe the energy spectrum of charmonium. The nonrelativistic limit is considered for the relativistic effects to be estimated in a self-consistent way and it is shown that the given effects could be extremely important for both the energy spectrum and the confinement mechanism.

The confinement mechanism proposed earlier by the author is applied to estimate the possible parameters of the confining SU(3)-gluonic field in an η ′ -meson. For this aim the electric form factor of an η ′ -meson is nonperturbatively computed in an explicit analytic form. The estimates obtained are also consistent with the width of the electromagnetic decay η ′ → 2γ. The corresponding estimates of the gluon concentrations, electric and magnetic colour field strengths are also adduced for the mentioned field at the scales of the meson under consideration.

The confinement mechanism proposed earlier by the author is applied to estimate the possible parameters of the confining SU (3)-gluonic field in an ηmeson. For this aim the electric form factor of an η -meson is nonperturbatively computed in an explicit analytic form. The estimates obtained are also consistent with the width of the electromagnetic decay η → 2γ . The corresponding estimates of the gluon concentrations, electric and magnetic colour field strengths are also adduced for the mentioned field at the scales of the meson under consideration.