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Relations between Limit-Point and Dirichlet Properties of Second-Order Difference Operators

Advances in Difference Equations volume 2007, Article number: 094325 (2007) Cite this article

Abstract

We consider second-order difference expressions, with complex coefficients, of the form acting on infinite sequences. The discrete analog of some known relationships in the theory of differential operators such as Dirichlet, conditional Dirichlet, weak Dirichlet, and strong limit-point is considered. Also, connections and some relationships between these properties have been established.

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References

  1. Amos RJ: On a Dirichlet and limit-circle criterion for second-order ordinary differential expressions. Quaestiones Mathematicae 1978,3(1):53–65. 10.1080/16073606.1978.9631559

    Article  MATH  MathSciNet  Google Scholar 

  2. Brown BM, Evans WD: On an extension of Copson's inequality for infinite series. Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1992,121(1–2):169–183. 10.1017/S0308210500014219

    Article  MATH  MathSciNet  Google Scholar 

  3. Chen J, Shi Y: The limit circle and limit point criteria for second-order linear difference equations. Computers & Mathematics with Applications 2004,47(6–7):967–976. 10.1016/S0898-1221(04)90080-6

    Article  MATH  MathSciNet  Google Scholar 

  4. Delil A, Evans WD: On an inequality of Kolmogorov type for a second-order difference expression. Journal of Inequalities and Applications 1999,3(2):183–214. 10.1155/S1025583499000132

    MATH  MathSciNet  Google Scholar 

  5. Evans WD, Everitt WN: A return to the Hardy-Littlewood integral inequality. Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1982,380(1779):447–486. 10.1098/rspa.1982.0052

    Article  MATH  MathSciNet  Google Scholar 

  6. Hinton DB, Lewis RT: Spectral analysis of second order difference equations. Journal of Mathematical Analysis and Applications 1978,63(2):421–438. 10.1016/0022-247X(78)90088-4

    Article  MATH  MathSciNet  Google Scholar 

  7. Kwong MK: Conditional Dirichlet property of second order differential expressions. The Quarterly Journal of Mathematics 1977,28(3):329–338. 10.1093/qmath/28.3.329

    Article  MATH  MathSciNet  Google Scholar 

  8. Kwong MK: Note on the strong limit point condition of second order differential expressions. The Quarterly Journal of Mathematics 1977,28(110):201–208.

    Article  MATH  MathSciNet  Google Scholar 

  9. Race D: On the strong limit-point and Dirichlet properties of second order differential expressions. Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1985,101(3–4):283–296. 10.1017/S0308210500020837

    Article  MATH  MathSciNet  Google Scholar 

  10. Sun S, Han Z, Chen S: Strong limit point for linear Hamiltonian difference system. Annals of Differential Equations 2005,21(3):407–411.

    MATH  MathSciNet  Google Scholar 

  11. Atkinson FV: Discrete and Continuous Boundary Problems, Mathematics in Science and Engineering. Volume 8. Academic Press, New York, NY, USA; 1964:xiv+570.

    Google Scholar 

  12. Delil A: İkinci mertebe fark ifadesinin Dirichlet ve limit-nokta özellikleri. 17th National Symposium of Mathematics, August 2004, Bolu, Turkey 26–31.

    Google Scholar 

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Authors and Affiliations

  1. Eǧitim Fakültesi, Celal Bayar Üniversitesi, 45900, Demirci, Manisa, Turkey

    A. Delil

  2. Dedicated to Professor W. D. Evans on the occasion of his 65th birthday, UK

    A. Delil

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  1. A. Delil
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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Delil, A. Relations between Limit-Point and Dirichlet Properties of Second-Order Difference Operators. Adv Differ Equ 2007, 094325 (2007). https://doi.org/10.1155/2007/94325

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  • DOI: https://doi.org/10.1155/2007/94325

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