Asymptotic and Oscillatory Behaviour of Third Order Non-linear Differential Equations with Canonical Operator and Mixed Neutral Terms

• Autores: J. Alzabut, Said R. Grace, S.S. Santra, G. N. Chhatria
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 22, Nº 1, 2023
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • This paper deals with the asymptotic and oscillatory behaviour of third-order nonlinear differential equations with mixed non-linear neutral terms and a canonical operator. The results are obtained via utilising integral conditions as well as comparison theorems with the oscillatory properties of first-order advanced and/or delay differential equations. The proposed theorems improve, extend, and simplify existing ones in the literature. The results are illustrated by two numerical examples.

• Referencias bibliográficas
  • 1. Agarwal, R.P., Grace, S.R., O’Regan, D.: Oscillation Theory for Difference and Functional Differential Equations. Kluwer Academic Publishers,...
  • 2. Agarwal, R.P., Grace, S.R., O’Regan, D.: Oscillation Theory for Second Order Linear, Half-Linear. Superlinear and Sublinear Dynamic Equations....
  • 3. Alzabut, J., Agarwal, R.P., Grace, S.R., Jonnalagadda, J.M.: Oscillation results for solutions of fractional-order differential equations....
  • 4. Agarwal, R.P., Grace, S.R.: Oscillation theorems for certain functional differential equations of higher order. Math. Comput. Model. 39,...
  • 5. Agarwal, R.P., Grace, S.R., Dontha, S.: On the oscillation of certain functional differential equations. Commun. Korean Math. Soc. 19,...
  • 6. Agarwal, R.P., Bohner, M., Li, T., Zhang, C.: A new approach in the study of oscillatory behaviour of even-order neutral delay differential...
  • 7. Alzabut, J., Bohner, M., Grace, S.R.: Oscillation of nonlinear third-order difference equations with mixed neutral terms. Adv. Differ....
  • 8. Alzabut, J., Grace, S.R., Chhatria, G.N.: New oscillation results for higher order nonlinear differential equations with a nonlinear neutral...
  • 9. Bainov, D.D., Mishev, D.P.: Oscillation Theory of Neutral Differential Equations with Delay. Adam Hilger Ltd., Bristol (1991)
  • 10. Baculíková, B.: Properties of third-order nonlinear functional differential equations with mixed arguments. Abstr. Appl. Anal. 2011, 857860...
  • 11. Baculíková, B., Džurina, J.: Oscillation of third-order neutral differential equations. Math. Comput. Model. 52, 215–226 (2010)
  • 12. Baculíková, B., Džurina, J.: On the asymptotic behavior of a class of third order nonlinear neutral differential equations. Cent. Eur....
  • 13. Baculíková, B., Džurina, J.: Oscillation theorems for higher order neutral differential equations. Appl. Math. Comput. 219, 3769–3778...
  • 14. Chatzarakis, G., Grace, S.R.: Third-order nonlinear differential equations with nonlinear neutral terms. Funct. Differ. Equ. 27, 3–13...
  • 15. Chatzarakis, G.E., Srinivasan, R., Thandapani, E.: Oscillation results for third-order quasi-linear Emden-Fowler differential equations...
  • 16. Došlá, Z., Liška, P.: Comparison theorems for third-order neutral differential equations. Electron. J. Differ. Equ. 2016, 38 (2016)
  • 17. Došlá, Z., Liška, P.: Oscillation of third-order nonlinear neutral differential equations. Appl. Math. Let. 56, 42–48 (2016)
  • 18. Džurina, J., Kotorová, R.: Properties of the third order trinomial differential equations with delay argument. Nonlinear Anal. 71, 1995–2002...
  • 19. Džurina, J., Grace, S.R., Jadlovská, I.: On nonexistence of Kneser solutions of third-order neutral delay differential equations. Appl....
  • 20. Erbe, L.H., Kong, Q., Zhang, B.G.: Oscillation Theory for Functional Differential Equations. Marcel Dekker Inc., New York (1995)
  • 21. Feng, L., Han, Z.: oscillation of a class of third-order neutral differential equations with noncanonical operators. Bull. Malays. Math....
  • 22. Finizio, N., Ladas, G.: Ordinary Differential Equations with Modern Applications, 3rd edn. Wadsworth Pub. Co., Belmont (1988)
  • 23. Grace, S.R., Graef, J.R., El-Beltagy, M.A.: On the oscillation of third order neutral delay dynamic equations on time scales. Comput....
  • 24. Grace, S.R., Graef, J.R., Tunç, E.: Oscillatory behaviour of third order nonlinear differential equations with a nonlinear nonpositive...
  • 25. Grace, S.R., Jadlovská, I.: Oscillatory behavior of odd-order nonlinear differential equations with a nonpositive Neutral term Dyn. Syst....
  • 26. Graef, J.R., Saker, S.H.: Oscillation theory of third-order nonlinear functional differential equations. Hiroshima Math. J. 43, 49–72...
  • 27. Graef, J.R., Tunç, E., Grace, S.R.: Oscillatory and asymptotic behavior of a third-order nonlinear neutral Differential equation. Opusc....
  • 28. Graef, J.R., Grace, S.R., Tunç, E.: Oscillation of even-order advanced functional differential equations. Publ. Math. Debrecen. 93, 445–455...
  • 29. Graef, J.R., Beldjerd, D., Remili, M.: On the stability, boundedness, and square integrability of solutions of third order neutral delay...
  • 30. Hale, J.K., Lunel, S.M.V.: Introduction to Functional Differential Equations. Springer, New York (1993)
  • 31. Hardy, G.H., Littlewood, I.E., Polya, G.: Inequalities. Cambridge University Press, Cambridge (1959)
  • 32. Jiang, Y., Jiang, C., Li, T.: Oscillatory behavior of third-order nonlinear neutral delay differential equations. Adv. Differ. Equ. 2016,...
  • 33. Karpuz, B., Öcalan, Ö., Özt ¯urk, S.: Comparison theorems on the oscillation and asymptotic behaviour of higher-order neutral differential...
  • 34. Kiguradze, I.T., Chanturia, T.A.: Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations. Kluwer Academic...
  • 35. Kitamura, Y., Kusano, T.: Oscillation of first-order nonlinear differential equations with deviating arguments. Proc. Am. Math. Soc. 78,...
  • 36. Koplatadze, R.G., Chanturiya, T.A.: Oscillating and monotone solutions of first-order differential equations with deviating argument(in...
  • 37. Ladas, G., Stavroulakis, I.P.: Oscillations caused by several retarded and advanced arguments. J. Differ. Equ. 44, 134–152 (1982)
  • 38. Li, T., Rogovchenko, Y.V.: On the asymptotic behavior of solutions to a class of third-order nonlinear neutral differential equations....
  • 39. Özdemir, O., Kaya, ¸S: Comparison theorems on the oscillation of third-order functional differential equations with mixed deviating arguments...
  • 40. Padhi, S., Pati, S.: Theory of Third-Order Differential Equations. Springer, New Delhi (2014)
  • 41. Philos, C.G.: On the existence of nonoscillatory solutions tending to zero at 1 for differential equations with positive delays. Arch....
  • 42. Saker, S.H., Alzabut, J., Mukheimer, A.: On the oscillatory behavior for a certain class of third order nonlinear delay difference equations....
  • 43. Thandapani, E., Li, T.: On the oscillation of third-order quasi-linear neutral functional differential equations. Arch. Math. (Brno) 47,...
  • 44. Thandapani, E., El-Sheikh, M.A.A., Sallam, R., Salem, S.: On the oscillatory behavior of third order differential equations with a sublinear...
  • 45. Tunç, E., ¸Sahin, S., Graef, J.R., Pinelas, S.: New oscillation criteria for third-order differential equations with bounded and unbounded...