Geodesic
Asymptotics of the eigenvalues of a boundary value problem~for the operator Schr\"{o}dinger equation with~boundary conditions nonlinearly dependent on~the~spectral parameter
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 25 (2021) no. 4, pp. 607-615

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On the space $H_{1}=L_{2}(H, [ 0, 1 ] )$, where $H$ is a separable Hilbert space, we study the asymptotic behavior of the eigenvalues of a boundary value problem for the operator Schrödinger equation for the case when one, and the same, spectral parameter participates linearly in the equation and quadratically in the boundary condition. Asymptotic formulae are obtained for the eigenvalues of the considered boundary value problem.
Keywords: operator differential equations, spectrum, eigenvalue, asymptotic formula, Hilbert space. 
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     title = {Asymptotics of the eigenvalues of a boundary value problem~for the operator {Schr\"{o}dinger} equation with~boundary conditions nonlinearly dependent on~the~spectral parameter},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
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I. F. Hashimoglu. Asymptotics of the eigenvalues of a boundary value problem~for the operator Schr\"{o}dinger equation with~boundary conditions nonlinearly dependent on~the~spectral parameter. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 25 (2021) no. 4, pp. 607-615. http://geodesic.mathdoc.fr/item/VSGTU_2021_25_4_a0/