Oscillation of certain difference equations

Said R. Grace

Czechoslovak Mathematical Journal (2000)

  • Volume: 50, Issue: 2, page 347-358
  • ISSN: 0011-4642

Abstract

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Some new criteria for the oscillation of difference equations of the form Δ 2 x n - p n Δ x n - h + q n | x g n | c s g n x g n = 0 and Δ i x n + p n Δ i - 1 x n - h + q n | x g n | c s g n x g n = 0 , i = 2 , 3 , are established.

How to cite

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Grace, Said R.. "Oscillation of certain difference equations." Czechoslovak Mathematical Journal 50.2 (2000): 347-358. <http://eudml.org/doc/30566>.

@article{Grace2000,
abstract = {Some new criteria for the oscillation of difference equations of the form \[ \Delta ^2 x\_n - p\_n \Delta x\_\{n-h\} + q\_n |x\_\{g\_n\}|^c \mathop \{\mathrm \{s\}gn\}x\_\{g\_n\} = 0 \] and \[ \Delta ^i x\_n + p\_n \Delta ^\{i-1\} x\_\{n-h\} + q\_n |x\_\{g\_n\}|^c \mathop \{\mathrm \{s\}gn\}x\_\{g\_n\} = 0, \ i = 2,3, \] are established.},
author = {Grace, Said R.},
journal = {Czechoslovak Mathematical Journal},
keywords = {difference equations; oscillation},
language = {eng},
number = {2},
pages = {347-358},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Oscillation of certain difference equations},
url = {http://eudml.org/doc/30566},
volume = {50},
year = {2000},
}

TY - JOUR
AU - Grace, Said R.
TI - Oscillation of certain difference equations
JO - Czechoslovak Mathematical Journal
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 50
IS - 2
SP - 347
EP - 358
AB - Some new criteria for the oscillation of difference equations of the form \[ \Delta ^2 x_n - p_n \Delta x_{n-h} + q_n |x_{g_n}|^c \mathop {\mathrm {s}gn}x_{g_n} = 0 \] and \[ \Delta ^i x_n + p_n \Delta ^{i-1} x_{n-h} + q_n |x_{g_n}|^c \mathop {\mathrm {s}gn}x_{g_n} = 0, \ i = 2,3, \] are established.
LA - eng
KW - difference equations; oscillation
UR - http://eudml.org/doc/30566
ER -

References

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  1. On the oscillatory and asymptotic behavior of damped functional differential equations, Math. Japon. 36 (1991), 229–237. (1991) Zbl0732.34056MR1095734
  2. Oscillatory and asymptotic behavior of damped functional differential equations, Math. Nachr. 142 (1989), 279–305. (1989) Zbl0698.34060MR1017387
  3. Oscillation theorems for damped functional differential equations, Funkcial. Ekvac. 35 (1992), 261–278. (1992) Zbl0758.34053MR1189896
  4. Oscillation theorems for second order delay and neutral difference equations, Utilitas Math. 45 (1994), 197–211. (1994) MR1284030
  5. 10.1006/jmaa.1994.1346, J.  Math. Anal. Appl. 187 (1994), 91–106. (1994) MR1296607DOI10.1006/jmaa.1994.1346
  6. Oscillation Theory of Delay Differential Equations with Applications, Oxford University Press, Oxford, 1991. (1991) MR1168471
  7. 10.1016/0022-247X(83)90088-4, J. Math. Anal. Appl. 91 (1983), 9–29. (1983) MR0688528DOI10.1016/0022-247X(83)90088-4
  8. 10.1155/S0161171292000152, Internat. J. Math. & Math. Sci. 15 (1992), 129–142. (1992) MR1143937DOI10.1155/S0161171292000152
  9. 10.1016/0096-3003(94)90132-5, Appl. Math. Comput. 62 (1994), 47–60. (1994) MR1274100DOI10.1016/0096-3003(94)90132-5
  10. 10.1137/0510006, SIAM J. Math. Anal. 10 (1979), 55–61. (1979) Zbl0397.39001MR0516749DOI10.1137/0510006
  11. On oscillation of some difference equations, Funkcial. Ekvac. 34 (1991), 157–172. (1991) MR1116887
  12. Existence theorem for the difference equation y n + 1 - 2 y n + y n - 1 = h 2 f ( y n ) , Internat. J. Math. & Math. Sci. 3 (1990), 69–77. (1990) MR0576630

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