Boundary Value Problem For a Sturm-Liouville Operator With Piecewise Continuous Coefficient

Mamedov, Kh. R.; Cetinkaya, F. Ayca

doi:10.15672/hjms.2015449435

Cited by 9 publications

(8 citation statements)

References 20 publications

(29 reference statements)

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“…() Solvability of boundary value problems for differential equations with discontinuous coefficients were investigated by M. L. Rasulov() in monographs. Various spectral properties of boundary‐transmission problems and its applications were investigated by the authors of this study and some others (see, for example, previous works ()). Note that in the series of S. Yakubov and Y. Yakubov's works, an abstract theory of boundary value problems with an eigenvalue parameter in the boundary conditions has been constructed.…”

Section: Introductionmentioning

confidence: 94%

Solvability of fourth‐order Sturm‐Liouville problems with abstract linear functionals in boundary‐transmission conditions

Kandemir

Mukhtarov

2018

Math Methods in App Sciences

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This study deals with the solvability of one nonclassical boundary-value problem for fourth-order differential equation on two disjoint intervals I 1 = (−1, 0)and I 2 = (0, 1). The boundary conditions contain not only endpoints x = −1and x = 1but also a point of interaction x = 0, finite number internal points x jki ∈ I j and abstract linear functionals S k . So, our problem is not a pure differential one. We investigate such important properties as isomorphism, Fredholmness and coerciveness with respect to the spectral parameter. Note that the obtained results are new even in the case of the boundary conditions without internal points x jki and without abstract linear functionals S k .

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Section: Introductionmentioning

confidence: 94%

Solvability of fourth‐order Sturm‐Liouville problems with abstract linear functionals in boundary‐transmission conditions

Kandemir

Mukhtarov

2018

Math Methods in App Sciences

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“…Related works [11][12][13][14][15][16][17][18] are devoted to the study of the spectral properties of eigenvalues and eigenfunctions of the classical Sturm-Liouville problems (ie, when p(x) = 0 and Δ(x) ≡ 0).…”

Section: Formulation Of the Boundary-value-transmission Problemmentioning

confidence: 99%

Computation of eigenvalues and eigenfunctions of a Schrödinger‐type boundary‐value‐transmission problem with retarded argument

Şen

2018

Math Methods in App Sciences

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MSC Classification: 34L20; 35R10The purpose of this study is to investigate a Schrödinger type of boundary-value-transmission problem with retarded argument. By modifying some techniques of [S.B. Norkin, Differential equations of the second order with retarded argument, Translations of Mathematical Monographs, Vol. 31, AMS, Providence, RI, 1972] and suggesting own approaches, we find asymptotic formulas for the eigenvalues and eigenfunctions of the second-order differential equation with retarded argument, which includes the eigenparameter as a quadratic function. KEYWORDS asymptotics of eigenvalues and eigenfunctions, differential equation with retarded argument, transmission conditionsHere, q(x) is a real valued function and continuous in I with a finite limit q (b ± 0) = lim x→b±0 q(x); the real valued function Δ(x) ⩾ 0 continuous in I and has a finite limit c]; the real valued function p(x) is continuous in I such that p(b) = p(c) = p 0 (p 0 ∈ R); is a real eigenparameter; and , , ≠ 0 are arbitrary real numbers. 6604

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“…The one-dimensional timeindependent Schrödinger equation in quantum mechanics can be given as an example of SL equation. Significant results have been obtained by many mathematicians over the years regarding the SL equation (see [25][26][27][28][29][30][31][32][33][34][35][36]). This equation has not yet been addressed in multiplicative calculus.…”

Section: Introductionmentioning

confidence: 99%

A New Type of Sturm-Liouville Equation in the Non-Newtonian Calculus

Goktas

2021

Journal of Function Spaces

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In mathematical physics (such as the one-dimensional time-independent Schrödinger equation), Sturm-Liouville problems occur very frequently. We construct, with a different perspective, a Sturm-Liouville problem in multiplicative calculus by some algebraic structures. Then, some asymptotic estimates for eigenfunctions of the multiplicative Sturm-Liouville problem are obtained by some techniques. Finally, some basic spectral properties of this multiplicative problem are examined in detail.

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Boundary Value Problem For a Sturm-Liouville Operator With Piecewise Continuous Coefficient

Cited by 9 publications

References 20 publications

Solvability of fourth‐order Sturm‐Liouville problems with abstract linear functionals in boundary‐transmission conditions

Solvability of fourth‐order Sturm‐Liouville problems with abstract linear functionals in boundary‐transmission conditions

Computation of eigenvalues and eigenfunctions of a Schrödinger‐type boundary‐value‐transmission problem with retarded argument

A New Type of Sturm-Liouville Equation in the Non-Newtonian Calculus

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