On the oscillation of Volterra summation equations

Ethiraju Thandapani; K. Ravi

Mathematica Bohemica (2001)

  • Volume: 126, Issue: 1, page 41-52
  • ISSN: 0862-7959

Abstract

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The asymptotic and oscillatory behavior of solutions of Volterra summation equations y n = p n ± ∑ s = 0 n - 1 K ( n , s ) f ( s , y s ) , n ∈ ℕ where ℕ = { 0 , 1 , 2 , ⋯ } , are studied. Examples are included to illustrate the results.

How to cite

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Thandapani, Ethiraju, and Ravi, K.. "On the oscillation of Volterra summation equations." Mathematica Bohemica 126.1 (2001): 41-52. <http://eudml.org/doc/248839>.

@article{Thandapani2001,
abstract = {The asymptotic and oscillatory behavior of solutions of Volterra summation equations \[ y\_\{n\}=p\_\{n\} \pm \sum \_\{s=0\}^\{n-1\}K(n,s)f(s,y\_\{s\}), \ n\in \mathbb \{N\} \] where $\mathbb \{N\}=\lbrace 0,1,2,\dots \rbrace $, are studied. Examples are included to illustrate the results.},
author = {Thandapani, Ethiraju, Ravi, K.},
journal = {Mathematica Bohemica},
keywords = {Volterra summation equations; oscillation; asymptotic behavior; Volterra summation equations; oscillation; asymptotic behavior},
language = {eng},
number = {1},
pages = {41-52},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the oscillation of Volterra summation equations},
url = {http://eudml.org/doc/248839},
volume = {126},
year = {2001},
}

TY - JOUR
AU - Thandapani, Ethiraju
AU - Ravi, K.
TI - On the oscillation of Volterra summation equations
JO - Mathematica Bohemica
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 126
IS - 1
SP - 41
EP - 52
AB - The asymptotic and oscillatory behavior of solutions of Volterra summation equations \[ y_{n}=p_{n} \pm \sum _{s=0}^{n-1}K(n,s)f(s,y_{s}), \ n\in \mathbb {N} \] where $\mathbb {N}=\lbrace 0,1,2,\dots \rbrace $, are studied. Examples are included to illustrate the results.
LA - eng
KW - Volterra summation equations; oscillation; asymptotic behavior; Volterra summation equations; oscillation; asymptotic behavior
UR - http://eudml.org/doc/248839
ER -

References

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  1. Difference Equations and Inequalities, Marcel Dekker, New York, 1992. (1992) Zbl0925.39001MR1155840
  2. Advanced Topics in Diffference Equations, Kluwer Publ., Dordrecht, 1997. (1997) MR1447437
  3. Oscillatory behavior of solutions of Volterra summation equations, Appl. Math. Lett (to appear). (to appear) MR1750064
  4. Global Behavior of Nonlinear Difference Equations of Higher Order with Applications, Kluwer Publ., Dordrecht, 1993. (1993) MR1247956
  5. Periodicity and stability of linear Volterra difference systems, (to appear). (to appear) MR1260872
  6. Global stability of a nonlinear Volterra difference systems, Diff. Equations Dynam. Systems 2 (1994), 337–345. (1994) MR1386278
  7. 10.1016/0893-9659(94)90060-4, Appl. Math. Lett. 7 (1994), 89–93. (1994) MR1349901DOI10.1016/0893-9659(94)90060-4
  8. Theory of Difference Equations, Academic Press, New York, 1988. (1988) MR0939611
  9. Asymptotic properties of solutions of a Volterra integral equations with delay, An. Ştiinţ. Univ. Al. I. Cuza Iaşi Secţ. I a Mat. 30 (1984), 25–30. (1984) MR0800137

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