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The present paper gives a priori bounds on the possible non-real eigenvalues of regular indefinite Sturm-Liouville problems and obtains sufficient conditions for such problems to admit non-real eigenvalues.

Spectral Theory · Mathematics 2013-06-25 Jiangang Qi , Shaozhu Chen

We consider the determination of an unknown potential $q(x)$ form a fractional diffusion equation subject to overposed lateral boundary data. We show that this data allows recovery of two spectral sequences for the associated inverse…

Mathematical Physics · Physics 2018-11-15 William Rundell , Masahiro Yamamoto

We introduce and present the general solution of three two-term fractional differential equations of mixed Caputo/Riemann Liouville type. We then solve a Dirichlet type Sturm-Liouville eigenvalue problem for a fractional differential…

Classical Analysis and ODEs · Mathematics 2017-12-29 Mohammad Dehghan , Angelo B. Mingarelli

In recent years, there appeared a considerable interest in the inverse spectral theory for functional-differential operators with constant delay. In particular, it is well known that, for each fixed $\nu\in\{0,1\},$ the spectra of two…

Spectral Theory · Mathematics 2021-02-17 Nebojša Djurić , Sergey Buterin

Regular Sturm-Liouville problems with indefinite weight functions may possess finitely many non-real eigenvalues. In this note we prove explicit bounds on the real and imaginary parts of these eigenvalues in terms of the coefficients of the…

Spectral Theory · Mathematics 2013-06-04 Jussi Behrndt , Shaozhu Chen , Friedrich Philipp , Jiangang Qi

In this study we are concerned with a class of generalized BVP' s consisting of eigendependent boundary conditions and supplementary transmission conditions at finite number interior points. By modifying some techniques of classical…

Classical Analysis and ODEs · Mathematics 2013-04-17 Kadriye Aydemir

In this work, we use the \textit{regularized sampling method} to compute the eigenvalues of Sturm Liouville problems with discontinuity conditions inside a finite interval. We work out an example by computing a few eigenvalues and their…

Spectral Theory · Mathematics 2007-05-23 Bilal Chanane

One important innovation here is that for the Sturm-Liouville considered equation together with eigenparameter dependent boundary conditions and two supplementary transmission conditions at one interior point. We develop Green's function…

Classical Analysis and ODEs · Mathematics 2013-03-29 K. Aydemir , O. Sh. Mukhtarov

In this paper, we study an inverse problem for linear parabolic system with variable diffusion coefficients subject to dynamic boundary conditions. We prove a global Lipschitz stability for the inverse problem involving a simultaneous…

Analysis of PDEs · Mathematics 2022-01-04 E. M. Ait Ben Hassi , S. E. Chorfi , L. Maniar , O. Oukdach

Given a set of transmission eigenvalues, we describe the connection of such a set to the indicator functions in entire function theory. The indicator functions control the asymptotic growth rate of the solution of the Sturm-Liouville…

Analysis of PDEs · Mathematics 2012-04-26 Lung-Hui Chen

An inverse spectral problem for the Sturm-Liouville operator with a singular potential from the class $W_2^{-1}$ is solved by the method of spectral mappings. We prove the uniqueness theorem, develop a constructive algorithm for solution,…

Spectral Theory · Mathematics 2020-05-08 Natalia P. Bondarenko

We consider Sturm-Liouville problems with a discontinuity in an interior point, which are motivated by the inverse problems for the torsional modes of the Earth. We assume that the potential on the right half-interval and the coefficient in…

Spectral Theory · Mathematics 2019-04-24 Chuan-Fu Yang , Natalia Bondarenko

We consider a regular indefinite Sturm-Liouville problem with two self-adjoint boundary conditions, one being affinely dependent on the eigenparameter. We give sufficient conditions under which a basis of each root subspace for this…

Classical Analysis and ODEs · Mathematics 2012-06-11 Paul Binding , Branko Ćurgus

We study a Sturm-Liouville type eigenvalue problem for second-order differential equations on the infinite interval. Here the eigenfunctions are nonzero solutions exponentially decaying at infinity. We prove that at any discrete eigenvalue…

Dynamical Systems · Mathematics 2010-09-08 David Blazquez-Sanz , Kazuyuki Yagasaki

The Sturm-Liouville boundary value problem (SLBVP) stands as a fundamental cornerstone in the realm of mathematical analysis and physical modeling. Also known as the Sturm-Liouville problem (SLP), this paper explores the intricacies of this…

Classical Analysis and ODEs · Mathematics 2024-02-02 N. Karjanto , P. Sadhani

In the paper, Sturm--Liouville differential operators on time scales consisting of a finite number of isolated points and segments are considered. Such operators unify differential and difference operators. We obtain properties of their…

Spectral Theory · Mathematics 2020-08-10 Maria Kuznetsova

We consider a regular indefinite Sturm-Liouville problem with two self-adjoint boundary conditions affinely dependent on the eigenparameter. We give sufficient conditions under which the root vectors of this Sturm-Liouville problem can be…

Classical Analysis and ODEs · Mathematics 2012-06-11 Paul Binding , Branko Ćurgus

The Sturm-Liouville operator with singular potentials on the lasso graph is considered. We suppose that the potential is known a priori on the boundary edge, and recover the potential on the loop from a part of the spectrum and some…

Spectral Theory · Mathematics 2017-11-16 Chuan-Fu Yang , Natalia P. Bondarenko

In this paper, further to the point interaction method for inverse Sturm-Liouville problems on finite intervals firstly proposed in our previous work, we will continue to generalize this method to the inverse eigenvalue problems for…

Classical Analysis and ODEs · Mathematics 2025-10-13 Min Zhao , Jiangang Qi , Xiao Chen

We prove that the potential of a Sturm--Liouville operator depends analytically and Lipschitz continuously on the spectral data (two spectra or one spectrum and the corresponding norming constants). We treat the class of operators with…

Spectral Theory · Mathematics 2011-01-31 Rostyslav O. Hryniv