Ir al contenido

Documat

Oscillation Properties of Solutions of Second Order Neutral Dynamic Equations of Non-canonical Type on Time Scales

  • Grace, Said R. [1] ; Chhatria, G. N. [2] ; Abbas, Syed [3]
    1. [1] Cairo University

      Cairo University

      Egipto

    2. [2] Sambalpur University

      Sambalpur University

      India

    3. [3] Indian Institute of Technology
    Mostrar afiliaciones +
  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 1, 2022
  • Idioma: inglés
  • Enlaces
  • Resumen

    • In this paper, we study the oscillation for a class of second order sublinear and superlinear neutral dynamic equations on time scales. The tools used to prove results are the Krasnoselskii’s fixed point theorem and several inequalities. For results, the restriction that the solution be unbounded to make it oscillatory is required. But it is not required for the equation to be almost oscillatory. At the end, we give examples for illustrations. We point out that the results are new even for the cases T=R and T=Z.

  • Referencias bibliográficas
    • 1. Agarwal, R.P., Grace, S.R., O’Regan, D.: Oscillation Theory for Second Order Linear, Half-Linear, Superlinear and Sublinear Dynamic Equations....
    • 2. Agarwal, R.P., Bohner, M., Grace, S.R., O’Regan, D.: Discrete Oscillation Theory. Hindawi Publishing Corporation, New York (2005)
    • 3. Agarwal, R.P., Bohner, M., Li, T., Zhang, C.: Comparison theorems for oscillation of second-order neutral dynamic equations. Mediterr....
    • 4. Agarwal, R.P., Bohner, M., Li, T., Zhang, C.: Oscillation of second-order Emden–Fowler neutral delay differential equations. Ann. Mat....
    • 5. Agarwal, R.P., Zhang, C., Li, T.: Some remarks on oscillation of second order neutral differential equations. Appl. Math. Comput. 274,...
    • 6. Arul, R., Shobha, V.S., Thandapani, E.: New oscillation criteria for second order delay differential equations with nonpositive neutral...
    • 7. Bohner, M., Peterson, A.: Dynamic Equations on Time Scales: An Introduction with Applications. Birkhauser, Boston (2001)
    • 8. Bohner, M., Peterson, A.: Advances in Dynamic Equations on Time Scales. Birkhauser, Boston (2003)
    • 9. Bohner, M., Li, T.: Oscillation of second-order p-Laplace dynamic equations with a nonpositive neutral coefficient. Appl. Math. Lett. 37,...
    • 10. Bohner, M., Grace, S.R., Jadlovska, I.: Oscillation criteria for second order neutral delay differential equation. Electron. J. Qual....
    • 11. Bohner, M., Hassan, T.S., Li, T.: Fite–Hille–Wintner-type oscillation criteria for second-order halflinear dynamic equations with deviating...
    • 12. Bohner, M., El-Morshedy, H.A., Grace, S.R., Sager, I.: Oscillation of second-order nonlinear difference equations with sublinear neutral...
    • 13. Bohner, M., Grace, S.R., Jadlovska, I.: Sharp oscillation criteria for second-order neutral delay differential equations. Math. Methods...
    • 14. Dosly, O., Hilger, S.: A necessary and sufficient condition for oscillation of the Sturm–Liouville dynamic equation on time scales. J....
    • 15. Dzurina, J., Grace, S.R., Jadlovska, I., Li, T.: Oscillation criteria for second-order Emden–Fowler delay differential equations with...
    • 16. Gao, J., Wang, Q.R.: Existence of nonoscillatory solutions to second-order nonlinear neutral dynamic equations on time scales. Rocky Mt....
    • 17. Grace, S.R., Agarwal, R.P., Bohner, M., O’Regan, D.: Oscillation of second order strongly superlinear and strongly sublinear dynamic equations....
    • 18. Grace, S.R., Bohner, M., Agarwal, R.P.: On the oscillation of second-order half-linear dynamic equations. J. Differ. Equ. Appl. 15, 451–460...
    • 19. Grace, S.R., Graef, J.R.: Oscillatory behaviour of second order nonlinear differential equations with a sublinear neutral term. Math....
    • 20. Grace, S.R., Jadlovsk, I., Zafer, A.: On oscillation of second order delay differential equations with a sublinear neutral term. Mediterr....
    • 21. Grace, S.R., Chhatria, G.N., Abbas, S.: Second order oscillation of non-canonical functional dynamical equations on time scales. Math....
    • 22. Gy ˝ori, I., Ladas, G.: Oscillation Theory of Delay Differential Equations with Applications. Oxford University Press, London (1991)
    • 23. Hale, J.K.: Theory of Functional Differential Equations. Springer, New York (1977)
    • 24. Hilger, S.: Analysis on measure chains—a unified approach to continuous and discrete calculus. Results Math. 18(1), 18–56 (1990)
    • 25. Ji, T., Tang, S., Thandapani, E.: On oscillation of second order neutral dynamic equations. Adv. Differ. Equ. 2013, 340 (2013)
    • 26. Kusano, T., Akio, O., Hiroyuki, U.: On the oscillation of solutions of second order quasilinear ordinary differential equations. Hiroshima...
    • 27. Kusano, T., Marusiak, P.: Asymptotic properties of solutions of second order quasilinear functional differential equations of neutral...
    • 28. Li, T., Rogovchenko, Yu.V.: Oscillation of second-order neutral differential equations. Math. Nachr. 288, 1150–1162 (2015)
    • 29. Li, H., Zhao, Y., Han, Z.: New oscillation criterion for Emden–Fowler type nonlinear neutral delay differential equations. J. Appl. Math....
    • 30. Meng, F., Zheng, Z.: Recent development in oscillatory properties of certain differential equations. J. Appl. Anal. Comput. 8, 1282–1306...
    • 31. Moaaz, O., Bazighifan, O.: Oscillation criteria for second-order quasi-linear neutral functional differential equation. Discret. Contin....
    • 32. Moaaz, O., Elabbasy, E.M., Qaraad, B.: An improved approach for studying oscillation of generalized Emden–Fowler neutral differential...
    • 33. Ponnuraj, D., Srinivasan, S., Thandapani, E.: Oscillation of second order neutral type Emden–Fowler delay difference equations. Int. J....
    • 34. Prabaharan, N., Dharuman, C., Thandapani, E., Pinelas, S.: New oscillation criteria for second order quasilinear neutral delay differential...
    • 35. Saker, S.H.: Oscillation criteria for a second-order quasilinear neutral functional dynamic equation on time scales. Nelin. Kolyv. 13(3),...
    • 36. Saker, S.H., Grace, S.R.: Oscillation criteria for quasi-linear functional dynamic equations on time scales. Math. Slovaca 69, 501–524...
    • 37. Sudha, B., Tamilvanan, S., Rama, R., Thandapani, E.: Oscillation criteria of second order delay differential equations with nonpositive...
    • 38. Sui, Y., Han, Z.: Oscillation of second order neutral dynamic equations with deviating arguments on time scales. Adv. Differ. Equ. 2018,...
    • 39. Sui, Y., Han, Z.: Oscillation of second order nonlinear dynamic equations with a nonlinear neutral term on time scales. J. Appl. Anal....
    • 40. Sui, Y., Sun, S.: Oscillation of Emden–Fowler type nonlinear neutral delay dynamic equation on time scales. J. Appl. Math. Comput. 60,...
    • 41. Tao, C., Sun, T., He, Q.: Nonoscillation for higher order nonlinear delay dynamic equations on time scales. Adv. Differ. Equ. 2016, 1–11...
    • 42. Thandapani, E., Selvarangam, S.: Oscillation of second order Emden–Fowler type neutral difference equations. Dyn. Contin. Discret. Impuls....
    • 43. Thandapani, E., Selvarangam, S.: Oscillation theorems for second order quasilinear neutral difference equations. J. Math. Comput. Sci....
    • 44. Thandapani, E., Balasubramanian, V.: Some oscillation results for second order neutral type difference equations. Differ. Equ. Appl. 3,...
    • 45. Trench, W.F.: Canonical forms and principal systems for general disconjugate equations. Trans. Am. Math. Soc. 189, 319–327 (1973)
    • 46. Tripathy, A.K., Bhaskar, T.G.: Oscillation results for second order nonlinear neutral delay dynamic equations. Funct. Differ. Equ. 17,...
    • 47. Wang, D., Xu, Z.: Oscillation of second order quasilinear neutral delay difference equations. Acta Math. Appl. Sin. Engl. Ser. 27, 93–104...
    • 48. Wu, H., Erbe, L., Peterson, A.: Oscillation of solution to second order half-linear delay dynamic equations on time scales. Electron....
    • 49. Zhang, C., Agarwal, R.P., Bohner, M., Li, T.: Oscillation of second order nonlinear neutral dynamic equations with noncanonical operators....
    • 50. Zhang, M., Chena, W., El-Sheikhc, M.M.A., Sallamc, R.A., Hassand, A.M., Li, T.: New oscillation criteria for second-order nonlinear delay...
    • 51. Zhang, C., Li, T.: A note on the oscillation of second-order quasilinear neutral dynamic equations on time scales. J. Math. Sci. 246,...
    • 52. Zhu, Z.Q., Wang, Q.R.: Existence of nonoscillatory solutions to neutral dynamic equations on time scales. J. Math. Anal. Appl. 335, 751–762...
Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno