Oscillatory properties of third-order semi-canonical dynamic equations on time scales via canonical transformation

References

[1] Agarwal, R.—Bohner, M.—Li, T.—Zhang, C.: Hille and Nehari type criteria for third-order delay dynamic equations, J. Differ. Equ. Appl. 19(10) (2013), 1563–1579.10.1080/10236198.2013.766729Search in Google Scholar

[2] Agarwal, R.—Bohner, M.—Li, T.—Zhang, C.: A Philos-type theorem for third-order nonlinear retarded dynamic equations, Appl. Math. Comput. 249 (2014), 527–531.10.1016/j.amc.2014.08.109Search in Google Scholar

[3] Akin, E.—Hassan, T.: Comparison criteria for third-order functional dynamic equations with mixed nonlinearities, Appl. Math. Comput. 268 (2015), 169–185.10.1016/j.amc.2015.06.046Search in Google Scholar

[4] Alrashdi, H.—Albalawi, W.—Muhib, A.—Moaaz, O.—Elabbasy, E.: Kamenev-type criteria for testing the asymptotic behavior of solutions of third-order quasi-linear neutral differential equations, Mathematics 12(11) (2024), Art. 1734.10.3390/math12111734Search in Google Scholar

[5] Ayyappan, G.—Chatzarakis, G.—Gopal, T.—Thandapani, E.: Oscillation criteria of third-order nonlinear neutral delay difference equations with noncanonical operators, Appl. Anal. Discrete Math. 15(2) (2021), 413–425.10.2298/AADM200913011ASearch in Google Scholar

[6] Ayyappan, G.—Chatzarakis, G.—Kumar, T.—Thandapani, E.: Oscillatory properties of third-order semi-noncanonical nonlinear delay difference equations, Math. Bohem. 148(1) (2023), 35–47.10.21136/MB.2022.0036-21Search in Google Scholar

[7] Bohner, M.—Peterson, A.: Dynamic Equations on Time Scales: An Introduction with Applications, Springer, Berlin, 2001.10.1007/978-1-4612-0201-1Search in Google Scholar

[8] Bohner, M.—Peterson, A.: Advances in Dynamic Equations on Time Scales, Springer, Berlin, 2002.10.1007/978-0-8176-8230-9Search in Google Scholar

[9] Chandrasekaran, E.—Chatzarakis, G.—Sakthivel, R.—Thandapani, E.: Third-order nonlinear semi-canonical functional differential equations: oscillation via new canonical transform, Mathematics 12(19) (2024), Art. 3113.10.3390/math12193113Search in Google Scholar

[10] Chandrasekaran, E.—Chatzarakis, G.—Sakthivel, R.—Thandapani, E.: Results on oscillatory properties of third-order functional difference equations with semi-canonical operators, Math. Slovaca 75(2) (2025), 353–368.10.1515/ms-2025-0027Search in Google Scholar

[11] Chatzarakis, G.—Džurina, J.—Jadlovská, I.: Oscillatory and asymptotic properties of third-order quasilinear delay differential equations, J. Inequal. Appl. 2019 (2019), Art. 48.10.1186/s13660-019-1967-0Search in Google Scholar

[12] Chatzarakis, G.—Grace, S.—Jadlovská, I.: Oscillation criteria for third-order delay differential equations, Adv. Differ. Equ. 2017 (2017), Art. 207.10.1186/s13662-017-1384-ySearch in Google Scholar

[13] Erbe, L.—Peterson, A.—Saker, S.: Asymptotic behavior of solutions of a third-order nonlinear dynamic equation on time scales, J. Comput. Appl. Math. 181(1) (2005), 92–102.10.1016/j.cam.2004.11.021Search in Google Scholar

[14] Grace, S.—Chhatria, G.: On oscillatory behaviour of third-order half-linear dynamic equations on time scales, Opusc. Math. 42(6) (2022), 849–865.10.7494/OpMath.2022.42.6.849Search in Google Scholar

[15] Graef, J.: Canonical, noncanonical, and semicanonical third-order dynamic equations on time scales, Results Nonlinear Anal. 5(3) (2022), 273–278.10.53006/rna.1075859Search in Google Scholar

[16] Graef, J.—Grace, S.—Chhatria, G.: New oscillation criteria for third-order nonlinear functional differential equations, Electron. J. Qual. Theory Differ. Equ. 2024(70) (2024).10.14232/ejqtde.2024.1.70Search in Google Scholar

[17] Graef, J.—Jadlovská, I.: Canonical representation of third-order delay dynamic equations on time scales, Differ. Equ. Appl. 16(1) (2024), 1–20.10.7153/dea-2024-16-01Search in Google Scholar

[18] Hassan, A.—Cesarano, C.—Askar, S.—Alshamrani, A.: Oscillatory behavior of solutions of third-order semi-canonical dynamic equations on time scale, AIMS Math. 9(9) (2024), 24213–24228.10.3934/math.20241178Search in Google Scholar

[19] Hassan, S.: Oscillation of third-order nonlinear delay dynamic equations on time scales, Math. Comput. Modelling 49(7–8) (2009), 1573–1586.10.1016/j.mcm.2008.12.011Search in Google Scholar

[20] Hassan, T.—Agarwal, R.—Mohammed, W.: Oscillation criteria for third-order functional half-linear dynamic equations, Adv. Differ. Equ. 2017 (2017), Art. 211.10.1186/s13662-017-1164-8Search in Google Scholar

[21] Hassan, T.—Kachout, M.—El-Matary, B.—Iambor, L.—Odinaev, I.—Ali, A.: Improved Hille-type and Ohriska-type criteria for half-linear third-order dynamic equations, Mathematics 12(23) (2024), Art. 3740.10.3390/math12233740Search in Google Scholar

[22] Hassan, T.—Kong, Q.—El-Nabulsi, R.—Anukool, W.: New Hille-type and Ohriska-type criteria for nonlinear third-order dynamic equations, Math. 10(21) (2022), Art. 4143.10.3390/math10214143Search in Google Scholar

[23] Hilger, S.: Analysis on measure chains–a unified approach to continuous and discrete calculus, Results Math. 18(1–2) (1990), 18–56.10.1007/BF03323153Search in Google Scholar

[24] Jadlovská, I.—Li, T.: A note on the oscillation of third-order delay differential equations, Appl. Math. Lett. 167 (2025), Art. ID 109555.10.1016/j.aml.2025.109555Search in Google Scholar

[25] Li, T.—Acosta-Soba, D.—Columbu, A.—Viglialoro, G.: Dissipative gradient nonlinearities prevent δ-formations in local and nonlocal attraction–repulsion chemotaxis models, Stud. Appl. Math. 154(2) (2025), e70018.10.1111/sapm.70018Search in Google Scholar

[26] Li, T.—Frassu, S.—Viglialoro, G.: Combining effects ensuring boundedness in an attraction–repulsion chemotaxis model with production and consumption, Z. Angew. Math. Phys. 74(3) (2023), Art. 109.10.1007/s00033-023-01976-0Search in Google Scholar

[27] Li, T.—Pintus, N.—Viglialoro, G.: Properties of solutions to porous medium problems with different sources and boundary conditions, Z. Angew. Math. Phys. 70 (2019), 1–18.10.1007/s00033-019-1130-2Search in Google Scholar

[28] Li, T.—Rogovchenko, Y.: Oscillatory behavior of second-order nonlinear neutral differential equations, Abstr. Appl. Anal. 2014 (2014), Art. 291093.10.1186/1687-2770-2014-68Search in Google Scholar

[29] Li, T.—Rogovchenko, Y.: On the asymptotic behavior of solutions to a class of third-order nonlinear neutral differential equations, Appl. Math. Lett. 105 (2020), Art. 106293.10.1016/j.aml.2020.106293Search in Google Scholar

[30] Li, T.—Viglialoro, G.: Boundedness for a nonlocal reaction chemotaxis model even in the attraction-dominated regime, Differ. Integral Equ. 34(5) (2021), 315–336.10.57262/die034-0506-315Search in Google Scholar

[31] Prabaharan, N.—Madhan, M.—Thandapani, E.—Tunç, E.: Remarks on the oscillation of nonlinear third-order noncanonical delay differential equations, Appl. Math. Comput. 481 (2024), Art. 128950.10.1016/j.amc.2024.128950Search in Google Scholar

[32] Qiu, Y.—Chiu, K.—Grace, S.—Liu, Q.—Jadlovská, I.: Oscillation of solutions to third-order nonlinear neutral dynamic equations on time scales, Mathematics 10(1) (2021), Art. 86.10.3390/math10010086Search in Google Scholar

[33] Salem, S.—Hassan, A.: Oscillatory behavior of solutions of third-order nonlinear neutral delay dynamic equations on time scales, Mediterr. J. Math. 20(6) (2023), Art. 308.10.1007/s00009-023-02506-ySearch in Google Scholar

[34] Saranya, K.—Piramanantham, V.—Thandapani, E.: Oscillation results for third-order semi-canonical quasi-linear delay differential equations, Nonauton. Dyn. Syst. 8(1) (2021), 228–238.10.1515/msds-2020-0135Search in Google Scholar

[35] Saranya, K.—Piramanantham, V.—Thandapani, E.—Tunç, E.: Asymptotic behavior of semi-canonical third-order nonlinear functional differential equations, Palest. J. Math. 11(3) (2022), 433–442.Search in Google Scholar

[36] Soliman, A.—Hassan, A.—Affan, S.: New oscillation criteria for second-order neutral delay dynamic equations with a nonpositive neutral term on time scales, Benha J. Appl. Sci. 5(7) (2020), 183–187.10.21608/bjas.2020.226977Search in Google Scholar

[37] Srinivasan, R.—Saravanan, S.—Thandapani, E.—Tunç, E.: Oscillation of noncanonical third-order delay differential equations via canonical transform, Appl. Math. E-Notes 23 (2023), 265–273.Search in Google Scholar

[38] Suresh, K.—Purushothaman, G.—Thandapani, E.—Tunç, E.: New and improved oscillation criteria of third-order half-linear delay differential equations via canonical transform, Math. Slovaca 75(2) (2025), 329–338.10.1515/ms-2025-0025Search in Google Scholar

[39] Thandapani, E.—Göktürk, B.—Özdemir, O.—Tunç, E.: Oscillatory behavior of semi-canonical nonlinear neutral differential equations of third-order via comparison principles, Qual. Theory Dyn. Syst. 22(1) (2023), Art. 30.10.1007/s12346-022-00731-6Search in Google Scholar