대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제52권1호
  • /
  • Pages.159-172
  • /
  • 2015
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

OSCILLATION CRITERIA FOR DIFFERENCE EQUATIONS WITH SEVERAL OSCILLATING COEFFICIENTS

  • Bohner, Martin (Department of Mathematics and Statistics Missouri University of Science and Technology) ;
  • Chatzarakis, George E. (Department of Electrical and Electronic Engineering Educators School of Pedagogical and Technological Education (ASPETE)) ;
  • Stavroulakis, Ioannis P. (Department of Mathematics University of Ioannina)
  • 투고 : 2013.12.04
  • 발행 : 2015.01.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

This paper presents a new sufficient condition for the oscillation of all solutions of difference equations with several deviating arguments and oscillating coefficients. Corresponding difference equations of both retarded and advanced type are studied. Examples illustrating the results are also given.

키워드

참고문헌

  1. R. P. Agarwal, M. Bohner, S. R. Grace, and D. O'Regan, Discrete Oscillation Theory, Hindawi Publishing Corporation, New York, 2005.
  2. M. Bohner, G. E. Chatzarakis, and I. P. Stavroulakis, Qualitative behavior of solutions of difference equations with several oscillating coefficients, Arab. J. Math. 3 (2014), no. 3, 1-13. https://doi.org/10.1007/s40065-013-0087-9
  3. G. E. Chatzarakis, S. Pinelas, and I. P. Stavroulakis, Oscillation of difference equations with several deviated arguments, Aequat. Math. 88 (2014), 105-123. https://doi.org/10.1007/s00010-013-0238-2
  4. N. Fukagai and T. Kusano, Oscillation theory of first order functional-differential equations with deviating arguments, Ann. Mat. Pura Appl. (4) 136 (1984), 95-117. https://doi.org/10.1007/BF01773379
  5. M. K. Grammatikopoulos, R. Koplatadze, and I. P. Stavroulakis, On the oscillation of solutions of first-order differential equations with retarded arguments, Georgian Math. J. 10 (2003), no. 1, 63-76.
  6. I. Gyori and G. Ladas, Oscillation Theory of Delay Differential Equations, Clarendon Press, Oxford, 1991.
  7. H. Khatibzadeh, An oscillation criterion for a delay difference equation, Comput. Math. Appl. 57 (2009), no. 1, 37-41. https://doi.org/10.1016/j.camwa.2008.07.041
  8. M. R. Kulenovic and M. K. Grammatikopoulos, First order functional differential inequalities with oscillating coefficients, Nonlinear Anal. 8 (1984), no. 9, 1043-1054. https://doi.org/10.1016/0362-546X(84)90098-1
  9. G. Ladas, G. Sficas, and I. P. Stavroulakis, Functional-differential inequalities and equations with oscillating coefficients, Trends in theory and practice of nonlinear differential equations (Arlington, Tex., 1982), 277-284, Lecture Notes in Pure and Appl. Math., 90, Marcel Dekker, New York, 1984.
  10. V. Lakshmikantham and D. Trigiante, Theory of Difference Equations: Numerical Methods and Applications, Mathematics in Science and Engineering, 181, Academic Press, Boston, MA, 1998.
  11. X. Li, D. Zhu and H. Wang, Oscillation for advanced differential equations with oscillating coefficients, Int. J. Math. Math. Sci. 2003 (2003), no. 33, 2109-2118. https://doi.org/10.1155/S0161171203209030
  12. C. Qian, G. Ladas, and J. Yan, Oscillation of difference equations with oscillating coefficients, Rad. Mat. 8 (1992), no. 1, 55-65.
  13. X. H. Tang and S. S. Cheng, An oscillation criterion for linear difference equations with oscillating coefficients, J. Comput. Appl. Math. 132 (2001), no. 2, 319-329. https://doi.org/10.1016/S0377-0427(00)00436-2
  14. T. Xianhua, Oscillation of first order delay differential equations with oscillating coefficients, Appl. Math. J. Chinese Univ. Ser. B 15 (2000), no. 3, 252-258. https://doi.org/10.1007/s11766-000-0048-x
  15. W. Yan and J. Yan, Comparison and oscillation results for delay difference equations with oscillating coefficients, Internat. J. Math. Math. Sci. 19 (1996), no. 1, 171-176. https://doi.org/10.1155/S0161171296000245
  16. J. S. Yu and X. H. Tang, Sufficient conditions for the oscillation of linear delay difference equations with oscillating coefficients, J. Math. Anal. Appl. 250 (2000), no. 2, 735-742. https://doi.org/10.1006/jmaa.2000.7120

피인용 문헌

  1. Oscillation results for difference equations with oscillating coefficients vol.2015, pp.1, 2015, https://doi.org/10.1186/s13662-015-0391-0