This article is cited in 2 papers

Spectral problem generated by the equation of smooth string with piece-wise constant friction

L. Kobyakova

South Ukrainian National Pedagogical University, 26 Staroportofrankivska St., Odesa, 65020, Ukraine

Abstract: In the paper, the spectral problem generated by the Sturm–Liouville equation
$$ - y'' + q(x) y = (\lambda^2 - i p(x) \lambda) y, $$
where $q(x)$ is a real $L_2(0,a)$-function and $p(x)$ is a peace-wise constant, is considered with the Dirichlet boundary conditions at the ends of the interval $(0,a)$. The spectrum of the problem is compared with the spectra of auxiliary problems with the Dirichlet–Dirichlet and the Dirichlet–Neumann boundary conditions on the halves of the interval. Asymptotic formulas are obtained for the eigenvalues of this problem.

Key words and phrases: spectral problem, Sturm–Liouville equation, eigenvalues.

MSC: 34B08, 47A75

Received: 03.10.2011

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