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## Asymptotics of the Hartree-type operator spectrum near the lower boundaries of spectral clusters

Applicable Analysis. 2016. Vol. 95. No. 7. P. 1560-1569.

We consider the eigenvalue problem for a perturbed two-dimensional

resonance oscillator. The excitation potential is given by a Hartree-type

nonlinearity with a smooth self-action potential. We use asymptotic

formulas for the quantum averages to obtain asymptotic eigenvalues and

asymptotic eigenfunctions near the lower boundaries of spectral clusters

which are formed near the energy levels of the unperturbed operator.