81
Views
0
CrossRef citations to date
0
Altmetric
Articles

Asymptotic summation of perturbed linear difference systems in critical case

Pages 1173-1199 | Received 01 Apr 2019, Accepted 24 Aug 2019, Published online: 05 Sep 2019

References

  • J. Baštinec, L. Berezansky, J. Diblík and Z. Šmarda, A final result on the oscillation of solutions of the linear discrete delayed equation Δx(n)=−p(n)x(n−k) with a positive coefficient, Abstr. Appl. Anal. 2011 (2011). Article ID 586328.
  • J. Baštinec and J. Diblík, Remark on positive solutions of discrete equation Δu(k+n)=−p(k)u(k), Nonlinear Anal. 63(5–7) (2005), pp. e2145–e2151. doi: 10.1016/j.na.2005.01.007
  • J. Baštinec, J. Diblík and Z. Šmarda, Existence of positive solutions of discrete linear equations with a single delay, J. Differ. Equ. Appl. 16(9) (2010), pp. 1047–1056. doi: 10.1080/10236190902718026
  • Z. Benzaid and D.A. Lutz, Asymptotic representation of solutions of perturbed systems of linear difference equations, Stud. Appl. Math. 77 (1987), pp. 195–221. doi: 10.1002/sapm1987773195
  • S. Bodine and D.A. Lutz, Asymptotic Integration of Differential and Difference Equations, Springer, New York, 2015.
  • V. Burd and P. Nesterov, Asymptotic behaviour of solutions of the difference Schrödinger equation, J. Differ. Equ. Appl. 17(11) (2011), pp. 1555–1579. doi: 10.1080/10236191003685908
  • J. Carr, Applications of Centre Manifold Theory, Springer-Verlag, New York, 1981.
  • J. Diblík, Asymptotic behavior of solutions of discrete equations, Funct. Differ. Equ. 11(1–2) (2004), pp. 37–48.
  • S. Elaydi, An Introduction to Difference Equations, 3rd ed., Springer, New York, 2005.
  • R. Graham, D. Knuth and O. Patashnik, Concrete Mathematics. A Foundation for Computer Science, 2nd ed., Addison-Wesley Publishing Company, Inc., Reading, MA, 1994.
  • I. Györi and M. Pituk, Asymptotic formulae for the solutions of a linear delay difference equation, J. Math. Anal. Appl. 195 (1995), pp. 376–392. doi: 10.1006/jmaa.1995.1361
  • I. Györi and M. Pituk, Stability criteria for linear delay differential equations, Differ. Integral Equ. 10(5) (1997), pp. 841–852.
  • I. Györi and M. Pituk, Asymptotic formulas for a scalar linear delay differential equation, Electron. J. Qual. Theory Differ. Equ. 72 (2016), pp. 1–14.
  • J.K. Hale, Theory of Functional Differential Equations, Springer-Verlag, New York, 1977.
  • N. Levinson, The asymptotic nature of solutions of linear systems of differential equations, Duke Math. J. 15(1) (1948), pp. 111–126. doi: 10.1215/S0012-7094-48-01514-2
  • J.E. Marsden and M. McCracken, The Hopf Bifurcation and Its Applications, Springer-Verlag, New York, 1976.
  • P. Nesterov, Asymptotic integration of functional differential systems with oscillatory decreasing coefficients: a center manifold approach, Electron. J. Qual. Theory Differ. Equ. 33 (2016), pp. 1–43. doi: 10.14232/ejqtde.2016.1.33
  • P. Nesterov, Asymptotic integration of a certain second-order linear delay differential equation, Monatsh. Math. 182(1) (2017), pp. 77–98. doi: 10.1007/s00605-016-0980-3
  • P. Nesterov, On some extension of center manifold method to functional differential equations with oscillatory decreasing coefficients and variable delays, J. Dynam. Differ. Equ. 30(4) (2018), pp. 1797–1816. doi: 10.1007/s10884-017-9628-9
  • K. Yosida, Functional Analysis, 6th ed., Springer-Verlag, Berlin, 1980.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.