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Regular version of the site

Article

Asymptotics of the spectrum of a two-dimensional Hartree-type operator with Coulomb self-action potential near the lower boundaries of spectral clusters

Theoretical and Mathematical Physics. 2019. Vol. 199. No. 3. P. 864-877.
D. A. Vakhrameeva, A. V. Pereskokov.

We consider the eigenvalue problem for a perturbed two-dimensional oscillator where the perturbation is an

integral Hartree-type nonlinearity with a Coulomb self-action potential. We obtain asymptotic eigenvalues

and asymptotic eigenfunctions near the lower boundaries of spectral clusters formed in a neighborhood of

the eigenvalues of the unperturbed operator and construct an asymptotic expansion near a circle where

the solution is localized.

We consider the eigenvalue problem for a perturbed two-dimensional oscillator where the perturbation is an

integral Hartree-type nonlinearity with a Coulomb self-action potential. We obtain asymptotic eigenvalues

and asymptotic eigenfunctions near the lower boundaries of spectral clusters formed in a neighborhood of

the eigenvalues of the unperturbed operator and construct an asymptotic expansion near a circle where

the solution is localized.

We consider the eigenvalue problem for a perturbed two-dimensional oscillator where the perturbation is an

integral Hartree-type nonlinearity with a Coulomb self-action potential. We obtain asymptotic eigenvalues

and asymptotic eigenfunctions near the lower boundaries of spectral clusters formed in a neighborhood of

the eigenvalues of the unperturbed operator and construct an asymptotic expansion near a circle where

 

the solution is localized.

We consider the eigenvalue problem for a perturbed two-dimensional oscillator where the perturbation is an

 

integral Hartree-type nonlinearity with a Coulomb self-action potential. We obtain asymptotic eigenvalues

 

and asymptotic eigenfunctions near the lower boundaries of spectral clusters formed in a neighborhood of

 

the eigenvalues of the unperturbed operator and construct an asymptotic expansion near a circle where

 

the solution is localized.

 

We consider the eigenvalue problem for a perturbed two-dimensional oscillator where the perturbation is an

integral Hartree-type nonlinearity with a Coulomb self-action potential. We obtain asymptotic eigenvalues

and asymptotic eigenfunctions near the lower boundaries of spectral clusters formed in a neighborhood of

the eigenvalues of the unperturbed operator and construct an asymptotic expansion near a circle where

the solution is localized.

We consider the eigenvalue problem for a perturbed two-dimensional oscillator where the perturbation is an

integral Hartree-type nonlinearity with a Coulomb self-action potential. We obtain asymptotic eigenvalues

and asymptotic eigenfunctions near the lower boundaries of spectral clusters formed in a neighborhood of

the eigenvalues of the unperturbed operator and construct an asymptotic expansion near a circle where

 

the solution is localized.

We consider the eigenvalue problem for a perturbed two-dimensional oscillator where the perturbation is an

 

integral Hartree-type nonlinearity with a Coulomb self-action potential. We obtain asymptotic eigenvalues

 

and asymptotic eigenfunctions near the lower boundaries of spectral clusters formed in a neighborhood of

 

the eigenvalues of the unperturbed operator and construct an asymptotic expansion near a circle where

 

the solution is localized.

 

We consider the eigenvalue problem for a perturbed two-dimensional oscillator where the perturbation is an

integral Hartree-type nonlinearity with a Coulomb self-action potential. We obtain asymptotic eigenvalues

and asymptotic eigenfunctions near the lower boundaries of spectral clusters formed in a neighborhood of

the eigenvalues of the unperturbed operator and construct an asymptotic expansion near a circle where

the solution is localized.

We consider the eigenvalue problem for a perturbed two-dimensional oscillator where the perturbation is an

integral Hartree-type nonlinearity with a Coulomb self-action potential. We obtain asymptotic eigenvalues

and asymptotic eigenfunctions near the lower boundaries of spectral clusters formed in a neighborhood of

the eigenvalues of the unperturbed operator and construct an asymptotic expansion near a circle where

the solution is localized.

We consider the eigenvalue problem for a perturbed two-dimensional oscillator where the perturbation is an

integral Hartree-type nonlinearity with a Coulomb self-action potential. We obtain asymptotic eigenvalues

and asymptotic eigenfunctions near the lower boundaries of spectral clusters formed in a neighborhood of

the eigenvalues of the unperturbed operator and construct an asymptotic expansion near a circle where

 

the solution is localized.

We consider the eigenvalue problem for a perturbed two-dimensional oscillator where the perturbation is an

 

integral Hartree-type nonlinearity with a Coulomb self-action potential. We obtain asymptotic eigenvalues

 

and asymptotic eigenfunctions near the lower boundaries of spectral clusters formed in a neighborhood of

 

the eigenvalues of the unperturbed operator and construct an asymptotic expansion near a circle where

 

the solution is localized.

 

We consider the eigenvalue problem for a perturbed two-dimensional oscillator where the perturbation is an

integral Hartree-type nonlinearity with a Coulomb self-action potential. We obtain asymptotic eigenvalues

and asymptotic eigenfunctions near the lower boundaries of spectral clusters formed in a neighborhood of

the eigenvalues of the unperturbed operator and construct an asymptotic expansion near a circle where

the solution is localized.