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Periodic solutions for nonlinear nonmonotone evolution inclusions
Qualitative properties of solutions of higher order difference equations with deviating arguments
Institute of Mathematics, Poznań University of Technology, Piotrowo 3A, 60-965 Poznań, Poland |
$(-1)^z Δ^m x(n)=f(n, x(σ_1(n)),x(σ_2(n)),..., x(σ_k(n)))$ |
$σ_i$ |
References:
[1] |
R. P. Agarwal, M. Bohner, S. R. Grace and D. O'Regan,
Discrete Oscillation Theory Hindawi Publishing Corporation, New York, 2005.
doi: 10.1155/9789775945198. |
[2] |
R. P. Agarwal,
Difference Equations and Inequalities. Theory, Methods, and Applications Second Edition, Revised and Expanded, Marcel Dekker, New York, 2000. |
[3] |
J. Baštinec, L. Berezansky, J. Diblík and Z. šmarda, A final result on the oscillation of solutions of the linear discrete delayed equation $Δ x(n)=-p(n)x(n-k)$ with a positive coefficient Abstract and Applied Analysis 2011 (2011), Art. ID 586328, 28 pp.
doi: 10.1155/2011/586328. |
[4] |
G. E. Chatzarakis, R. Koplatadze and I. P. Stavroulakis,
Oscillation criteria of first order linear difference equations with delay argument, Nonlinear Anal., 68 (2008), 994-1005.
doi: 10.1016/j.na.2006.11.055. |
[5] |
G. E. Chatzarakis, M. Lafci and I. P. Stavroulakis,
Oscillation results for difference equations with several oscillating coefficients, Applied Mathematics and Computation, 251 (2015), 81-91.
doi: 10.1016/j.amc.2014.11.045. |
[6] |
G. E. Chatzarakis, Ch. G. Philos and I. P. Stavroulakis,
On the oscillation of the solutions to linear difference equations with variable delay, Electron. J. Differ. Equ., 50 (2008), 1-15.
|
[7] |
G. E. Chatzarakis and Ö. Öcalan,
Oscillation of difference equations with non-monotone retarded arguments, Applied Mathematics and Computation, 258 (2015), 60-66.
doi: 10.1016/j.amc.2015.01.110. |
[8] |
G. E. Chatzarakis, H. Péics, S. Pinelas and I. P. Stavroulakis, Oscillation results for difference equations with oscillating coefficients Advances in Difference Equations 2015 (2015), 17pp.
doi: 10.1186/s13662-015-0391-0. |
[9] |
L. H. Erbe and B. G. Zhang,
Oscillation of discrete analogues of delay equations, Differential Integral Equations, 2 (1989), 300-309.
|
[10] |
G. Grzegorczyk and J. Werbowski,
On oscillatory solutions of certain difference equations, Opuscula Mathematica, 26 (2006), 317-326.
|
[11] |
G. Grzegorczyk and J. Werbowski,
Oscillation of higher-order linear difference equations, Comput. Math. Appl., 42 (2001), 711-717.
doi: 10.1016/S0898-1221(01)00190-0. |
[12] |
I. Györi and G. Ladas,
Oscillation Theory of Delay Differential Equations with Applications Clarendon Press, Oxford, New York, 1991. |
[13] |
W. G. Kelley and A. C. Peterson,
Difference Equations. An Introduction with Applications Second edition, Harcourt/Academic Press, San Diego, CA, 2001. |
[14] |
G. Ladas, Ch. G. Philos and Y. G. Sficas,
Sharp conditions for the oscillation of delay difference equations, J. Appl. Math. Simulation, 2 (1989), 101-111.
doi: 10.1155/S1048953389000080. |
[15] |
J. Migda, Approximative solutions of difference equations,
Electron. J. Qual. Theory Differ. Equ. 13 (2014), 26 pp. |
[16] |
M. Migda,
Existence of nonoscillatory solutions of some higher order difference equations, Appl. Math. E-Notes, 4 (2004), 33-39.
|
[17] |
M. Migda and J. Migda,
On the asymptotic behavior of solutions of higher order nonlinear difference equations, Nonlinear Analysis, 47 (2001), 4687-4695.
doi: 10.1016/S0362-546X(01)00581-8. |
[18] |
M. Migda,
Asymptotic properties of nonoscillatory solutions of higher order neutral difference equations, Opuscula Mathematica, 26 (2006), 507-514.
|
[19] |
W. Nowakowska and J. Werbowski,
On connections between oscillatory solutions of functional, difference and differential equations, Fasc. Math., 44 (2010), 95-106.
|
[20] |
Ch. G. Philos, I. K. Purnaras and I. P. Stavroulakis,
Sufficient conditions for the oscillation of delay difference equations, J. Difference Equ. Appl., 10 (2004), 419-435.
doi: 10.1080/10236190410001648239. |
[21] |
J. Werbowski,
Bounded oscillations of differential equations generated by deviating arguments, Utilitas Math., 31 (1987), 191-198.
|
[22] |
A. Wyrwińska,
Oscillation criteria of a higher order linear difference equation, Bull. Inst. Math. Acad. Sinica, 22 (1994), 259-266.
|
show all references
References:
[1] |
R. P. Agarwal, M. Bohner, S. R. Grace and D. O'Regan,
Discrete Oscillation Theory Hindawi Publishing Corporation, New York, 2005.
doi: 10.1155/9789775945198. |
[2] |
R. P. Agarwal,
Difference Equations and Inequalities. Theory, Methods, and Applications Second Edition, Revised and Expanded, Marcel Dekker, New York, 2000. |
[3] |
J. Baštinec, L. Berezansky, J. Diblík and Z. šmarda, A final result on the oscillation of solutions of the linear discrete delayed equation $Δ x(n)=-p(n)x(n-k)$ with a positive coefficient Abstract and Applied Analysis 2011 (2011), Art. ID 586328, 28 pp.
doi: 10.1155/2011/586328. |
[4] |
G. E. Chatzarakis, R. Koplatadze and I. P. Stavroulakis,
Oscillation criteria of first order linear difference equations with delay argument, Nonlinear Anal., 68 (2008), 994-1005.
doi: 10.1016/j.na.2006.11.055. |
[5] |
G. E. Chatzarakis, M. Lafci and I. P. Stavroulakis,
Oscillation results for difference equations with several oscillating coefficients, Applied Mathematics and Computation, 251 (2015), 81-91.
doi: 10.1016/j.amc.2014.11.045. |
[6] |
G. E. Chatzarakis, Ch. G. Philos and I. P. Stavroulakis,
On the oscillation of the solutions to linear difference equations with variable delay, Electron. J. Differ. Equ., 50 (2008), 1-15.
|
[7] |
G. E. Chatzarakis and Ö. Öcalan,
Oscillation of difference equations with non-monotone retarded arguments, Applied Mathematics and Computation, 258 (2015), 60-66.
doi: 10.1016/j.amc.2015.01.110. |
[8] |
G. E. Chatzarakis, H. Péics, S. Pinelas and I. P. Stavroulakis, Oscillation results for difference equations with oscillating coefficients Advances in Difference Equations 2015 (2015), 17pp.
doi: 10.1186/s13662-015-0391-0. |
[9] |
L. H. Erbe and B. G. Zhang,
Oscillation of discrete analogues of delay equations, Differential Integral Equations, 2 (1989), 300-309.
|
[10] |
G. Grzegorczyk and J. Werbowski,
On oscillatory solutions of certain difference equations, Opuscula Mathematica, 26 (2006), 317-326.
|
[11] |
G. Grzegorczyk and J. Werbowski,
Oscillation of higher-order linear difference equations, Comput. Math. Appl., 42 (2001), 711-717.
doi: 10.1016/S0898-1221(01)00190-0. |
[12] |
I. Györi and G. Ladas,
Oscillation Theory of Delay Differential Equations with Applications Clarendon Press, Oxford, New York, 1991. |
[13] |
W. G. Kelley and A. C. Peterson,
Difference Equations. An Introduction with Applications Second edition, Harcourt/Academic Press, San Diego, CA, 2001. |
[14] |
G. Ladas, Ch. G. Philos and Y. G. Sficas,
Sharp conditions for the oscillation of delay difference equations, J. Appl. Math. Simulation, 2 (1989), 101-111.
doi: 10.1155/S1048953389000080. |
[15] |
J. Migda, Approximative solutions of difference equations,
Electron. J. Qual. Theory Differ. Equ. 13 (2014), 26 pp. |
[16] |
M. Migda,
Existence of nonoscillatory solutions of some higher order difference equations, Appl. Math. E-Notes, 4 (2004), 33-39.
|
[17] |
M. Migda and J. Migda,
On the asymptotic behavior of solutions of higher order nonlinear difference equations, Nonlinear Analysis, 47 (2001), 4687-4695.
doi: 10.1016/S0362-546X(01)00581-8. |
[18] |
M. Migda,
Asymptotic properties of nonoscillatory solutions of higher order neutral difference equations, Opuscula Mathematica, 26 (2006), 507-514.
|
[19] |
W. Nowakowska and J. Werbowski,
On connections between oscillatory solutions of functional, difference and differential equations, Fasc. Math., 44 (2010), 95-106.
|
[20] |
Ch. G. Philos, I. K. Purnaras and I. P. Stavroulakis,
Sufficient conditions for the oscillation of delay difference equations, J. Difference Equ. Appl., 10 (2004), 419-435.
doi: 10.1080/10236190410001648239. |
[21] |
J. Werbowski,
Bounded oscillations of differential equations generated by deviating arguments, Utilitas Math., 31 (1987), 191-198.
|
[22] |
A. Wyrwińska,
Oscillation criteria of a higher order linear difference equation, Bull. Inst. Math. Acad. Sinica, 22 (1994), 259-266.
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