Abstract
For the simplest Sturm–Liouville equation, we study a problem in which one boundary condition contains the squared spectral parameter and the other boundary condition is homogeneous. We find a condition on the physical parameter of the problem under which there arises a multiple eigenvalue. We consider a problem of mathematical physics for the heat operator which leads to the spectral problem studied in the paper.
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Kapustin, N.Yu., On the Uniform Convergence of the Fourier Series for a Spectral Problem with Squared Spectral Parameter in the Boundary Condition, Differ. Uravn., 2010, vol. 46, no. 10, pp. 1504–1507.
Kapustin, N.Yu., On the Uniform Convergence in the Class C 1 of the Fourier Series for a Spectral Problem with Squared Spectral Parameter in the Boundary Condition, Differ. Uravn., 2011, vol. 47, no. 10, pp. 1394–1399.
Moiseev, E.I. and Kapustin, N.Yu., On the Basis Property in the Space L p of Systems of Eigenfunctions Corresponding to Two Problems with Spectral Parameter in the Boundary Condition, Differ. Uravn., 2000, vol. 36, no. 10, pp. 1357–1360.
Kapustin, N.Yu., An a Priori Estimate for the Solution of a Mixed Problem for the Heat Equation, Differ. Uravn., 2006, vol. 42, no. 10, pp. 1375–1379.
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Original Russian Text © N.Yu. Kapustin, 2015, published in Differentsial’nye Uravneniya, 2015, Vol. 51, No. 10, pp. 1284–1289.
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Kapustin, N.Y. On the basis property of the system of eigenfunctions of a problem with squared spectral parameter in a boundary condition. Diff Equat 51, 1274–1279 (2015). https://doi.org/10.1134/S0012266115100031
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DOI: https://doi.org/10.1134/S0012266115100031