Asymptotics of the spectrum of a Hartree-type operator with a screened Coulomb self-action potential near the upper boundaries of spectral clusters

We consider the eigenvalue problem for a Hartree-type operator with a screened Coulomb self-action potential and with a small parameter multiplying the nonlinearity. We obtain asymptotic eigenvalues and asymptotic eigenfunctions near the upper boundaries of spectral clusters that form near the energy levels of the unperturbed operator.