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Keywords:
semi-noncanonical operator; third-order; delay difference equation; oscillation
semi-noncanonical operator; third-order; delay difference equation; oscillation
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.
References:
[1] Agarwal, R. P.: Difference Equations and Inequalities: Theory, Methods, and Applications. Pure and Applied Mathematics, Marcel Dekker 228. Marcel Dekker, New York (2000). DOI 10.1201/9781420027020 | MR 1740241 | Zbl 0952.39001
[2] Agarwal, R. P., Bohner, M., Grace, S. R., O'Regan, D.: Discrete Oscillation Theory. Hindawi Publications, New York (2005). DOI 10.1155/9789775945198 | MR 2179948 | Zbl 1084.39001
[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. DOI 10.1155/ADE.2005.345 | MR 2201689 | Zbl 1107.39004
[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. DOI 10.1007/s12190-009-0243-8 | MR 2578923 | Zbl 1191.39012
[5] Aktaş, M. F., Tiryaki, A., Zafer, A.: Oscillation of third-order nonlinear delay difference equations. Turk. J. Math. 36 (2012), 422-436. DOI 10.3906/mat-1010-67 | MR 2993574 | Zbl 1260.39015
[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. DOI 10.1186/s13662-020-03156-0 | MR 4196627
[7] Arul, R., Ayyappan, G.: Oscillation criteria for third order neutral difference equations with distributed delay. Malaya J. Mat. 1 (2013), 1-10. DOI 10.26637/mjm102/001 | Zbl 1369.39002
[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. MR 4182255 | Zbl 07429837
[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. DOI 10.18576/amis/110305 | MR 36488061
[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. DOI 10.1155/ADE/2006/65652 | MR 2209669 | Zbl 1133.39007
[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. DOI 10.26637/MJM0803/0100 | MR 4147103
[12] Grace, S. R., Agarwal, R. P., Aktas, M. F.: Oscillation criteria for third order nonlinear difference equations. Fasc. Math. 42 (2009), 39-51. MR 2573524 | Zbl 1186.39012
[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. DOI 10.2298/AADM0901027G | MR 2499304 | Zbl 1224.39016
[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. MR 1745309 | Zbl 1141.39301
[15] Banu, S. Mehar, Banu, M. Nazreen: Oscillatory behavior of half-linear third order delay differene equations. Malaya J. Matematik S (2021), 531-536. DOI 10.26637/MJMS2101/0122
[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.
[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. MR 2767893 | Zbl 1215.39015
[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. DOI 10.14232/ejqtde.2010.1.67 | MR 2735028 | Zbl 1208.39019
[19] Schmeidel, E.: Oscillatory and asymptotically zero solutions of third order difference equations with quasidifferences. Opusc. Math. 26 (2006), 361-369. MR 2272303 | Zbl 1133.39011
[20] Shoukaku, Y.: On the oscillation of solutions of first-order difference equations with delay. Commun. Math. Anal. 20 (2017), 62-67. MR 3744011 | Zbl 1383.39012
[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
[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. MR 2329832 | Zbl 1154.39302
[23] Thandapani, E., Selvarangam, S.: Oscillation theorems for second order quasilinear neutral difference equations. J. Math. Comput. Sci. 2 (2012), 866-879. MR 2947156
[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. DOI 10.21136/MB.2018.0019-17 | MR 3934196 | Zbl 07088834
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