q-Sturm-Liouville operator
Inverse spectral problem for Sturm Liouville operator with discontinuous coefficient and cubic polynomials of spectral parameter in boundary condition
... – f ˙ (x, λ) + q(x) ˙ f (x, λ) = λ ρ(x) ˙ f (x, λ) + λρ(x)f (x, λ), () here f ˙ denotes differentiation with respect to λ. Multiplying () by f ˙ (x, λ) and () by f (x, λ) and subtracting the second from ...
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Inverse problem for Sturm-Liouville operators with a transmission and parameter dependent boundary conditions
... self-adjoint Sturm–Liouville operator −D 2 + q with eigen- parameter dependent boundary and discontinuity conditions inside a finite closed ...
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Reconstruction of potential function for Sturm-Liouville operator with Coulomb potential
... the Sturm-Liouville operator with Coulomb potential using a new kind of spectral data that is known as nodal ...of q as a limit of a sequence of functions whose nth term is dependent only on ...
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Eigenfunction expansion in the singular case for q-Sturm-Liouville operators
... q − calculus, roughly speaking, is calculus without ordinary limits. It allows to deal with sets of not differentiable functions if the classical derivative is replaced with the q − derivative ...
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The inverse scattering problem of some Schrödinger type equation with turning point
... Inverse problems of spectral analysis consist in recovering operators from their spectral characteristics. Such problems often appear in mathematics, mechanics, physics, elec- tronics, geophysics, meteorology, and other ...
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Inverse Sturm-Liouville problems with transmission and spectral parameter boundary conditions
... transformation operator for inverse Sturm-Liouville problem with parameter dependent boundary and discon- tinuous ...for q(x) − q(x) in the ˜ finite interval, where ˜ q(x) is an ...
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On Summability of Spectral Expansions Corresponding to the Sturm Liouville Operator
... Theorems 4.2, 4.3, and 4.5 and the results of 36 imply that the whole class of regular but not strengthened regular boundary conditions splits into two subclasses a and b. Sub- class a coincides with the second type of ...
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An inverse spectral problem for the matrix Sturm-Liouville operator on the half-line
... scalar Sturm-Liouville operators –y +q(x)y (see monographs [–] and the references ...of Sturm-Liouville operators on the half -line has been achieved by Marchenko ...
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Spectral analysis of the matrix Sturm–Liouville operator
... matrix Sturm–Liouville operators in the form Y = –Y + Q(x)Y , where Q(x) is a matrix ...scalar Sturm–Liouville op- erators, which have been studied fairly completely (see the ...
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Existence of solutions for fractional Sturm-Liouville boundary value problems with \(p(t)\)-Laplacian operator
... Fredholm operator with index ...and Q : Y → Y , which meet the conditions that Im P = Ker L and KerQ = Im L, then L| domL∩KerP : dom L ∩ Ker P → Im L is ...
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Inverse problem for a class of Sturm-Liouville operator with spectral parameter in boundary condition
... This work aims to examine a Sturm-Liouville operator with a piece-wise continuous coefficient and a spectral parameter in boundary condition. The orthogonality of the eigenfunctions, realness and ...
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Inverse Nodal Problems for the Sturm Liouville Operator with Some Nonlocal Integral Conditions
... Sturm-Liouville operators have an important role in physics, mathematics and other engineering fields [1] [2] [3] [4] [5]. Nonlocal problems are parts of diffe- rential equation theory. And the inverse ...
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Asymptotic Behavior of Eigenvalue and Eigenfunction of a Six Order Boundary Value Problem
... the Sturm-Liouville operator generated by the separate boundary condition (Aigunov, 1996) and many researchers have found asymptotic formula for the Sturm-Liouville operator’s ...
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On a Boundary Value Problem for a Polynomial Pencil of the Sturm Liouville Equation with Spectral Parameter in Boundary Conditions
... [10] Guseinov, I.M., Nabiev, A.A. and Pashayev, R.T. (2000) Transformation Operators and Asymptotic Formulas for the Eigenvalues of a Polynomial Pencil of Sturm-Liouville Oper- ators. Siberian Journal of ...
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Sturm-Liouville theory
... continuous function on [0,C] can be expressed as a series in terms ofthe eigenfunctions.. In.[r] ...
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Eigenparameter dependent inverse boundary value problem for a class of Sturm-Liouville operator
... dependent Sturm-Liouville problems, ...the Sturm-Liouville problem but also in the boundary conditions, are given in ...discontinuous Sturm-Liouville problems are examined in ...
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Sampling theorem associated with q-Dirac system
... in q−Dirac system are few, see [1 − 3] ...with q−Dirac system do not exist as far as we ...a q−analogue of sampling theorem for q−Dirac system ...
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Extended Jacobi and Laguerre Functions and their Applications
... Abstract. The aim of this paper is to introduce two new extensions of the Jacobi and Laguerre polynomials as the eigenfunctions of two non- classical Sturm-Liouville problems. We prove some important ...
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Existence and iterative solutions of a new kind of Sturm-Liouville-type boundary value problem with one-dimensional p-Laplacian
... Boundary value problems (BVPs) have been studied for a long period. At the begin- ning, most researchers focused on two-point BVPs with four classical boundary con- ditions (BCs) of Dirichlet type u() = u() = , ...
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Perturbation Results of Limit point case and Limit circle case of Sturm-Liouville Differential Operators
... perturbation limit point case (limit circle case) for the Sturm-Liouville differential operator at a singular point remains invariant. Keywords : limit point case, limit circle case, sin[r] ...
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