| Title:
|
Oscillatory properties of third-order semi-noncanonical nonlinear delay difference equations (English) |
| Author:
|
Ayyappan, Govindasamy |
| Author:
|
Chatzarakis, George E. |
| Author:
|
Kumar, Thaniarasu |
| Author:
|
Thandapani, Ethiraj |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
148 |
| Issue:
|
1 |
| Year:
|
2023 |
| Pages:
|
35-47 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study the oscillatory properties of the solutions of the third-order nonlinear semi-noncanonical delay difference equation $$ D_3y(n)+f(n)y^\beta (\sigma (n))=0, $$ where $D_3 y(n)=\Delta (b(n)\Delta (a(n)(\Delta y(n))^\alpha ))$ is studied. The main idea is to transform the semi-noncanonical operator into canonical form. Then we obtain new oscillation theorems for the studied equation. Examples are provided to illustrate the importance of the main results. (English) |
| Keyword:
|
semi-noncanonical operator |
| Keyword:
|
third-order |
| Keyword:
|
delay difference equation |
| Keyword:
|
oscillation |
| MSC:
|
39A10 |
| idZBL:
|
Zbl 07655811 |
| idMR:
|
MR4536308 |
| DOI:
|
10.21136/MB.2022.0036-21 |
| . |
| Date available:
|
2023-02-03T11:20:23Z |
| Last updated:
|
2023-09-13 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151525 |
| . |
| Reference:
|
[1] Agarwal, R. P.: Difference Equations and Inequalities: Theory, Methods, and Applications.Pure and Applied Mathematics, Marcel Dekker 228. Marcel Dekker, New York (2000). Zbl 0952.39001, MR 1740241, 10.1201/9781420027020 |
| Reference:
|
[2] Agarwal, R. P., Bohner, M., Grace, S. R., O'Regan, D.: Discrete Oscillation Theory.Hindawi Publications, New York (2005). Zbl 1084.39001, MR 2179948, 10.1155/9789775945198 |
| Reference:
|
[3] Agarwal, R. P., Grace, S. R., O'Regan, D.: On the oscillation of certain third-order difference equations.Adv. Difference Equ. 2005 (2005), 345-367. Zbl 1107.39004, MR 2201689, 10.1155/ADE.2005.345 |
| Reference:
|
[4] Agarwal, R. P., Grace, S. R., Wong, P. J. Y.: On the oscillation of third order nonlinear difference equations.J. Appl. Math. Comput. 32 (2010), 189-203. Zbl 1191.39012, MR 2578923, 10.1007/s12190-009-0243-8 |
| Reference:
|
[5] Aktaş, M. F., Tiryaki, A., Zafer, A.: Oscillation of third-order nonlinear delay difference equations.Turk. J. Math. 36 (2012), 422-436. Zbl 1260.39015, MR 2993574, 10.3906/mat-1010-67 |
| Reference:
|
[6] Alzabut, J., Bohner, M., Grace, S. R.: Oscillation of nonlinear third-order difference equations with mixed neutral terms.Adv. Difference Equ. 2021 (2021), Article ID 3, 18 pages. MR 4196627, 10.1186/s13662-020-03156-0 |
| Reference:
|
[7] Arul, R., Ayyappan, G.: Oscillation criteria for third order neutral difference equations with distributed delay.Malaya J. Mat. 1 (2013), 1-10. Zbl 1369.39002, 10.26637/mjm102/001 |
| Reference:
|
[8] Ayyappan, G., Chatzarakis, G. E., Gopal, T., Thandapani, E.: On the oscillation of third-order Emden-Fowler type difference equations with unbounded neutral term.Nonlinear Stud. 27 (2020), 1105-1115. Zbl 07429837, MR 4182255 |
| Reference:
|
[9] Bohner, M., Dharuman, C., Srinivasan, R., Thandapani, E.: Oscillation criteria for third-order nonlinear functional difference equations with damping.Appl. Math. Inf. Sci. 11 (2017), 669-676. MR 36488061, 10.18576/amis/110305 |
| Reference:
|
[10] Došlá, Z., Kobza, A.: \kern-.635ptOn third-order linear difference equations involving quasi-differences.Adv. Difference Equ. 2006 (2006), Article ID 65652, 13 pages. Zbl 1133.39007, MR 2209669, 10.1155/ADE/2006/65652 |
| Reference:
|
[11] Gopal, T., Ayyapan, G., Arul, R.: Some new oscillation criteria of third-order half-linear neutral difference equations.Malaya J. Mat. 8 (2020), 1301-1306. MR 4147103, 10.26637/MJM0803/0100 |
| Reference:
|
[12] Grace, S. R., Agarwal, R. P., Aktas, M. F.: Oscillation criteria for third order nonlinear difference equations.Fasc. Math. 42 (2009), 39-51. Zbl 1186.39012, MR 2573524 |
| Reference:
|
[13] Grace, S. R., Agarwal, R. P., Graef, J. R.: Oscillation criteria for certain third order nonlinear difference equations.Appl. Anal. Discrete Math. 3 (2009), 27-38. Zbl 1224.39016, MR 2499304, 10.2298/AADM0901027G |
| Reference:
|
[14] Graef, J. R., Thandapani, E.: Oscillatory and asymptotic behavior of solutions of third order delay difference equations.Funkc. Ekvacioj, Ser. Int. 42 (1999), 355-369. Zbl 1141.39301, MR 1745309 |
| Reference:
|
[15] Banu, S. Mehar, Banu, M. Nazreen: Oscillatory behavior of half-linear third order delay differene equations.Malaya J. Matematik S (2021), 531-536. 10.26637/MJMS2101/0122 |
| Reference:
|
[16] Mohankumar, P., Ananthan, V., Ramesh, A.: Oscillation solution of third order nonlinear difference equations with delays.Int. J. Math. Comput. Research 2 (2014), 581-586. |
| Reference:
|
[17] Saker, S. H., Alzabut, J. O.: Oscillatory behavior of third order nonlinear difference equations with delayed argument.Dyn. Contin. Discrete Impuls. Syst., Ser. A., Math. Anal. 17 (2010), 707-723. Zbl 1215.39015, MR 2767893 |
| Reference:
|
[18] Saker, S. H., Alzabut, J. O., Mukheimer, A.: On the oscillatory behavior for a certain class of third order nonlinear delay difference equations.Electron. J. Qual. Theory Differ. Equ. 2010 (2010), Article ID 67, 16 pages. Zbl 1208.39019, MR 2735028, 10.14232/ejqtde.2010.1.67 |
| Reference:
|
[19] Schmeidel, E.: Oscillatory and asymptotically zero solutions of third order difference equations with quasidifferences.Opusc. Math. 26 (2006), 361-369. Zbl 1133.39011, MR 2272303 |
| Reference:
|
[20] Shoukaku, Y.: On the oscillation of solutions of first-order difference equations with delay.Commun. Math. Anal. 20 (2017), 62-67. Zbl 1383.39012, MR 3744011 |
| Reference:
|
[21] Srinivasan, R., Dharuman, C., Graef, J. R., Thandapani, E.: Oscillation and property (B) of third order delay difference equations with a damping term.Commun. Appl. Nonlinear Anal. 26 (2019), 55-67. MR 3967189 |
| Reference:
|
[22] Thandapani, E., Pandian, S., Balasubramaniam, R. K.: Oscillatory behavior of solutions of third order quasilinear delay difference equations.Stud. Univ. Žilina, Math. Ser. 19 (2005), 65-78. Zbl 1154.39302, MR 2329832 |
| Reference:
|
[23] Thandapani, E., Selvarangam, S.: Oscillation theorems for second order quasilinear neutral difference equations.J. Math. Comput. Sci. 2 (2012), 866-879. MR 2947156 |
| Reference:
|
[24] Vidhayaa, K. S., Dharuman, C., Thandapani, E., Pinelas, S.: Oscillation theorems for third order nonlinear delay difference equations.Math. Bohem. 144 (2019), 25-37. Zbl 07088834, MR 3934196, 10.21136/MB.2018.0019-17 |
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