# Asymptotics of the spectrum of the Sturm-Liouville operator with local interaction

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In this paper, we study the Sturm-Liouville operator with two interior discontinuities and with spectral parameter linearly contained in one of the boundary conditions. Spectral properties of the eigenvalues and norming constants of this operator are investigated. Moreover, the Weyl solution and...

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In this paper, we study unilateral global bifurcation which bifurcates from the trivial solutions axis or from infinity for nonlinear Sturm-Liouville problems of the form {-(pu')' + qu = Î» au + af (x, u, u', Î») + g (x, u, u', Î») for x âˆˆ (0, 1), b0 (0) + c0u' (0) = 0, b1u(1) + c1u...

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Inverse Sturm-Liouville problems with eigenparameter-dependent boundary conditions are considered. Theorems analogous to those of both Hochstadt and Gelfand and Levitan are proved.In particular, let ly = (1/r)((py2)2+qy), lÃœy = (1/rÃœ)((pÃœy2)2+qÃœy),formula herewhere det â€ = Â´...

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In this paper the Homotopy analysis method is applied to the nonlinear Sturm-Liouville problem-yâˆ³ + y(t)p = Î»(t); y(t) > 0; t Ïµ I = (0; 1); y(0) = y(1) = 0 where p > 1 is a constant and Î» > 0 is an eigenvalue parameter. Also, the eigenvalues and the behavior of eigenfunctions of...

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The article discusses the study which describes the spectrum of the Sturm-Liouville operator with degenerate boundary conditions. It considers the eigenvalue problem for the Sturm-Liouville equation on zero interval with degenerate boundary value problems. It details the the properties of the...

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In this study, Sturm-Liouville problem with discontinuities in the case when an eigenparameter linearly appears not only in the differential equation but it also appears in both of the boundary conditions is investigated.

- Necessary Conditions for the Localization of the Spectrum of the Sturm-Liouville Problem on a Curve. Ishkin, Kh. K. // Mathematical Notes;Jul/Aug2005, Vol. 78 Issue 1/2, p64
We consider the Sturm-Liouville operator on a convex smooth curve lying in the complex plane and connecting the points 0 and 1. We prove that if the eigenvalues Î»k with large numbers are localized near a single ray, then this ray is the positive real semiaxis. Moreover, if the eigenvalues...

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A new uniqueness theorem is established for the inverse Sturmâ€“Liouville problem. It is shown that the measurement of a particular eigenvalue for an infinite set of different boundary conditions is sufficient to determine the unknown potential.