Sturm–Liouville theory ≈ Sturm–Liouville theory
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Fundamental Results of Conformable Sturm-Liouville Eigenvalue Problems Open
We suggest a regular fractional generalization of the well-known Sturm-Liouville eigenvalue problems. The suggested model consists of a fractional generalization of the Sturm-Liouville operator using conformable derivative and with natural…
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Comparative simulations for solutions of fractional Sturm–Liouville problems with non-singular operators Open
In this study, we consider fractional Sturm–Liouville (S–L) problems within non-singular operators. A fractional S–L problem with exponential and Mittag-Leffler kernels is given with different versions in the Riemann–Liouville and Caputo s…
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AN INVERSE PROBLEMS FOR STURM-LIOUVILLE-TYPE DIFFERENTIAL EQUATION WITH A CONSTANT DELAY Open
The topic of this paper is non-self-adjoint second order differential operators with constant delay generated by -y + q(x)y(x -τ ) where potential q is complex-valued function, q ∈ L 2 [0, π] .We establish properties of the spectral charac…
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Systems of generalized Sturm-Liouville and Langevin fractional differential equations Open
In this paper, we study anti-periodic boundary value problems for systems of generalized Sturm-Liouville and Langevin fractional differential equations. Existence and uniqueness results are proved via fixed point theorems. Examples illustr…
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Sturm-Liouville differential operators with deviating argument Open
Non-selfadjoint second-order differential operators with a constant delay are studied. We establish properties of the spectral characteristics and investigate the inverse problem of recovering operators from their spectra. For this inverse…
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Fractional analogue of Sturm–Liouville operator Open
In this paper we study a symmetric fractional differential operator of order 2\alpha , (1/2<\alpha<1) . Using the extension theory a class of self-adjoint problems generated by the fractional Sturm–Liouville equation is described.
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An inverse problem for the Sturm-Liouville pencil with arbitrary entire functions in the boundary condition Open
The Sturm-Liouville pencil is studied with arbitrary entire functions of the spectral parameter, contained in one of the boundary conditions. We solve the inverse problem, that consists in recovering the pencil coefficients from a part of …
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Generalized Sturm-Liouville and Langevin equations via Hadamard fractional derivatives with anti-periodic boundary conditions Open
In this paper, we introduce a new class of anti-periodic boundary value problems by combining Sturm-Liouville and Langevin fractional differential equations of Hadamard type. Existence and uniqueness results are proved via fixed point theo…
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Variational principles for spectral analysis of one Sturm-Liouville problem with transmission conditions Open
We study certain spectral aspects of the Sturm-Liouville problem with a finite number of interior singularities. First, for self-adjoint realization of the considered problem, we introduce a new inner product in the direct sum of the …
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Inverse problems for Sturm-Liouville difference equations Open
We consider a discrete Sturm-Liouville problem with Dirichlet boundary conditions. We show that the specification of the eigenvalues and weight numbers uniquely determines the potential. Moreover, we also show that if the potential is symm…
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A 2-edge partial inverse problem for the Sturm-Liouville operators with singular potentials on a star-shaped graph Open
Boundary value problems for Sturm-Liouville operators with potentials from the class $W_2^{-1}$ on a star-shaped graph are considered. We assume that the potentials are known on all the edges of the graph except two, and show that the pote…
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The eigenvalue problem with interaction conditions at one interior singular point Open
Some physical processes, both classical physics and quantum physics reduced to eigenvalue problems for Sturm-Liouville equations. In the recent years there has been an increasing interest in discontinuous eigenvalue problems for various St…
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Existence and uniqueness of solution for Sturm–Liouville fractional differential equation with multi-point boundary condition via Caputo derivative Open
We investigate the existence and uniqueness of a solution for a Sturm–Liouville fractional differential equation with a multi-point boundary condition via the Caputo derivative; existence and uniqueness results for the given problem are ob…
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Exact and Numerical Solution of the Fractional Sturm–Liouville Problem with Neumann Boundary Conditions Open
In this paper, we study the fractional Sturm–Liouville problem with homogeneous Neumann boundary conditions. We transform the differential problem to an equivalent integral one on a suitable function space. Next, we discretize the integral…
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Scattering theory of impulsive Sturm-Liouville equations Open
In this paper, we investigate scattering theory of the impulsive Sturm-Liouville boundary value problem (ISBVP). In particular, we find the Jost solution and the scattering function of this problem. We also study the properties of the Jost…
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Qualitative analysis of eigenvalues and eigenfunctions of one boundary value-transmission problem Open
The aim of this study is to investigate various qualitative properties of eigenvalues and corresponding eigenfunctions of one Sturm-Liouville problem with an interior singular point. We introduce a new Hilbert space and integral operator i…
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Bounds on real and imaginary parts of non-real eigenvalues of a non-definite Sturm–Liouville problem Open
In this paper we obtain bounds on the real and imaginary parts of non-real eigenvalues of a non-definite Sturm–Liouville problem, with Dirichlet boundary conditions, that improve on corresponding results obtained in Behrndt et al., [7].
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Inverse Sturm–Liouville Problem with Spectral Parameter in the Boundary Conditions Open
In this paper, for the first time, we study the inverse Sturm–Liouville problem with polynomials of the spectral parameter in the first boundary condition and with entire analytic functions in the second one. For the investigation of this …
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The existence of solutions for Sturm–Liouville differential equation with random impulses and boundary value problems Open
In this article, we consider the existence of solutions to the Sturm–Liouville differential equation with random impulses and boundary value problems. We first study the Green function of the Sturm–Liouville differential equation with rand…
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Existence results of solution for fractional Sturm–Liouville inclusion involving composition with multi-maps Open
This paper is introduced as complementary studies based on fractional Sturm–Liouville problems in a Banach space. We explore the existence results for new considered problems which can be considered as mixture of equations and inclusions. …
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Ψ-Bielecki-type norm inequalities for a generalized Sturm–Liouville–Langevin differential equation involving Ψ-Caputo fractional derivative Open
The present research work investigates some new results for a fractional generalized Sturm–Liouville–Langevin (FGSLL) equation involving the Ψ -Caputo fractional derivative with a modified argument. We prove the uniqueness of the solution …
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Recovery of Inhomogeneity from Output Boundary Data Open
We consider the Sturm–Liouville equation on a finite interval with a real-valued integrable potential and propose a method for solving the following general inverse problem. We recover the potential from a given set of the output boundary …
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Spectrum curves for a discrete Sturm–Liouville problem with one integral boundary condition Open
This paper presents new results on the spectrum on complex plane for discrete Sturm–Liouville problem with one integral type nonlocal boundary condition depending on three parameters: γ, ξ1 and ξ2. The integral condition is approximated by…
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On a fractional hybrid version of the Sturm–Liouville equation Open
It is well known that the Sturm–Liouville equation has many applications in different areas of science. Thus, it is important to review different versions of the well-known equation. The technique of α -admissible α - ψ -contractions was i…
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On a Partial Fractional Hybrid Version of Generalized Sturm–Liouville–Langevin Equation Open
As we know one of the most important equations which have many applications in various areas of physics, mathematics, and financial markets, is the Sturm–Liouville equation. In this paper, by using the α-ψ-contraction technique in fixed po…
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On the spectral and scattering properties of eigenparameter dependent discrete impulsive Sturm–Liouville equations Open
This work develops scattering and spectral analysis of a discrete impulsive Sturm-Liouville equation with spectral parameter in boundary condition. Giving the Jost solution and scattering solutions of this problem, we find scattering funct…
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A source inverse problem for the pseudo–parabolic equation with the fractional Sturm–Liouville operator Open
A class of inverse problems for restoring the right-hand side of the pseudo-parabolic equation with one fractional Sturm–Liouville operator is considered. In this paper, we prove the existence and uniqueness results of the solutions using …
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Solutions of Sturm-Liouville Problems Open
This paper further improves the Lie group method with Magnus expansion proposed in a previous paper by the authors, to solve some types of direct singular Sturm–Liouville problems. Next, a concrete implementation to the inverse Sturm–Liouv…
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An expansion theorem for q -Sturm-Liouville operators on the whole line Open
In this work, we establish a Parseval equality and an expansion formula in eigenfunctions for a singular $q-$Sturm-Liouville operator on the whole line.
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ON A q-BOUNDARY VALUE PROBLEM WITH DISCONTINUITY CONDITIONS Open
In this paper, we studied q-analogue of Sturm–Liouville boundary value problem on a finite interval having a discontinuity in an interior point. We proved that the q-Sturm–Liouville problem is self-adjoint in a modified Hilbert space. We i…