Open Access

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

Advances in Difference Equations20072007:094325

DOI: 10.1155/2007/94325

Received: 24 July 2006

Accepted: 11 April 2007

Published: 21 June 2007


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.


Authors’ Affiliations

Eǧitim Fakültesi, Celal Bayar Üniversitesi
Dedicated to Professor W. D. Evans on the occasion of his 65th birthday


  1. Amos RJ: On a Dirichlet and limit-circle criterion for second-order ordinary differential expressions. Quaestiones Mathematicae 1978,3(1):53–65. 10.1080/16073606.1978.9631559MATHMathSciNetView ArticleGoogle 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/S0308210500014219MATHMathSciNetView ArticleGoogle 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)90080-6MATHMathSciNetView ArticleGoogle 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/S1025583499000132MATHMathSciNetGoogle 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.1982.0052MATHMathSciNetView ArticleGoogle 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)90088-4MATHMathSciNetView ArticleGoogle 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/28.3.329MATHMathSciNetView ArticleGoogle 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.MATHMathSciNetView ArticleGoogle 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/S0308210500020837MATHMathSciNetView ArticleGoogle 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.MATHMathSciNetGoogle 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


© A. Delil. 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.