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On stability and square integrability of solutions to some third order neutral differential equations

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Abstract

In this paper, the asymptotic behavior of solutions for a class of non-autonomous third order neutral delay differential equations is studied. Results on the stability, the boundedness and the square integrability of solutions and their derivatives are obtained. An example to illustrate the results is included.

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References

  1. Ademola, A.T., Mahmoud, A.M., Arawomo, P.O.: On the behaviour of solutions for a class of third order neutral delay differential equations. Anal. Univ. Oradea Fasc. Mate. Tom XXVI(2), 85–103 (2019)

    MathSciNet  MATH  Google Scholar 

  2. Arino, O., Hbid, M.L.: Ait Dads. Springer, Delay Differential Equations and Application. NATO Sciences series. Berlin (2006)

  3. Chatzarakis, G.E., Džurina, J., Jadlovská, I.: Oscillatory properties of third-order neutral delay differential equations with noncanonical operators. Mathematics 7, 1177 (2019)

    Article  Google Scholar 

  4. Graef, J.R., Oudjedi, L.D., Remili, M.: Stability and Square Integrability of solutions to third order neutral delay differential equations. Tatra Mt. Math. Publ. 71(1), 81–97 (2018)

    MathSciNet  MATH  Google Scholar 

  5. Graef, J.R., Beldjerd, D., Remili, M.: On stability, ultimate boundedness, and existence of periodic solutions of certain third order differential equations with delay. PanAmerican Math. J. 25, 82–94 (2015)

    MathSciNet  MATH  Google Scholar 

  6. Graef, J.R., Beldjerd, D., Remili, M.: Some new stability, boundedness, and square integrability conditions for third-order neutral delay differential equations. Commun. Math. Anal. 22(1), 76–89 (2019)

    MathSciNet  MATH  Google Scholar 

  7. Hale, J.K.: Theory of Functional Differential Equations. Springer, New York (1977)

    Book  Google Scholar 

  8. Hale, J.K., Lunel, S.M.V.: Introduction To Functional-Differential Equations. Springer, New York (1993)

    Book  Google Scholar 

  9. Kulenovic, M.R.S., Ladas, G., Meimaridou, A.: Stability of solutions of linear delay differential equations. Proc. Am. Math. Soc. 100, 433–441 (1987)

    Article  MathSciNet  Google Scholar 

  10. Khatir, A.M., Graef, J.R., Remili, M.: Stability, boundedness, and square integrability of solutions to third order neutral differential equations with delay. Rend. Circ. Mat. Palermo II Ser. 2019, 5 (2019). https://doi.org/10.1007/s12215-019-00438-9

    Article  MATH  Google Scholar 

  11. Li, T., Rogovchenko, Y.V.: On the asymptotic behavior of solutions to a class of third-order nonlinear neutral differential equations. Appl. Math. Lett. 105, 106293 (2020)

    Article  MathSciNet  Google Scholar 

  12. Li, T.-X., Zhang, C.-H., Xing, G.-J.: Oscillation of third-order neutral delay differential equations. Abstr. Appl. Anal. 2012, 11 (2012)

    MathSciNet  MATH  Google Scholar 

  13. Moaaz, O., Chalishajar, D., Bazighifan, O.: Asymptotic behavior of solutions of the third order nonlinear mixed type neutral differential equations. Mathematics 8, 485 (2020)

    Article  Google Scholar 

  14. Moulai-khatir, A., Remili, M., Beldjerd, D.: Stability, boundedness and square integrability of solutions to certain third order neutral delay differential equations. Palestine J. Math. 09(02), 880–890 (2020)

    MathSciNet  MATH  Google Scholar 

  15. Omeike, M.O.: New results on the asymptotic behavior of a third-order nonlinear differential equation. Differ. Equ. Appl. 2(1), 39–51 (2010)

    MathSciNet  MATH  Google Scholar 

  16. Omeike, M.O.: New results on the stability of solution of some non-autonomous delay differential equations of the third order. Differ. Equ. Control Process. 2010(1), 18–29 (2010)

    MathSciNet  MATH  Google Scholar 

  17. Oudjedi, L.D., Lekhmissi, B., Remili, M.: Asymptotic properties of solutions to third order neutral differential equations with delay. Proyecciones 38(1), 111–127 (2019)

    Article  MathSciNet  Google Scholar 

  18. Remili, M., Beldjerd, D.: On the asymptotic behavior of the solutions of third order delay differential equations. Rend. Circ. Mat. Palermo 63(3), 447–455 (2014)

    Article  MathSciNet  Google Scholar 

  19. Remili, M., Beldjerd, D.: A boundedness and stability results for a kind of third order delay differential equations. Appl. Appl. Math. 10(2), 772–782 (2015)

    MathSciNet  MATH  Google Scholar 

  20. Remili, M., Beldjerd, D.: Stability and ultimate boundedness of solutions of some third order differential equations with delay. J. Assoc. Arab Univ. Basic Appl. Sci. 23, 90–95 (2017)

    MATH  Google Scholar 

  21. Remili, M., Oudjedi, L.: Stability and boundedness of nonautonomous neutral differential equation with delay. Math. Moravica 24(1), 1–16 (2020)

    Article  MathSciNet  Google Scholar 

  22. Sun, Y., Zhao, Y.: Oscillatory behavior of third-order neutral delay differential equations with distributed deviating arguments. J. Inequal. Appl. 2019, 207 (2019)

    Article  MathSciNet  Google Scholar 

  23. Tian, Y.-Z., Cai, Y.-L., Fu, Y.-L., Li, T.-X.: Oscillation and asymptotic behavior of third-order neutral differential equations with distributed deviating arguments. Adv. Differ. Equ. 2015, 14 (2015)

    Article  MathSciNet  Google Scholar 

  24. Tunç, C.: Some stability and boundedness conditions for non-autonomous differential equations with deviating arguments. E. J. Qual. Theory Differ. Equ. 1, 1–12 (2010)

    MathSciNet  MATH  Google Scholar 

  25. Tunç, C.: New results about stability and boundedness of solutions of certain nonlinear third-order delay differential equations. Arab. J. Sci. Eng. Sect. A Sci. 31, 185–196 (2006)

    MathSciNet  MATH  Google Scholar 

  26. Tunç, C.: Stability and boundedness of the nonlinear differential equations of third order with multiple deviating arguments. Afr. Mat. 24(3), 381–390 (2013)

    Article  MathSciNet  Google Scholar 

  27. Tunç, C.: Stability and bounded of solutions to non-autonomous delay differential equations of third order. Nonlinear Dyn. 62(4), 945–953 (2010)

    Article  MathSciNet  Google Scholar 

  28. Tunç, C.: Global stability and boundedness of solutions to differential equations of third order with multiple delays. Dyn. Syst. Appl. 24(4), 467–478 (2015)

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University Oran 1 Ahmed Ben Bella, 31000, Oran, Algeria

    Amira Fellous & Moussadek Remili

  2. Institute of Maintenance and Industrial Safety, University of Oran 2 Mohamed Ben Ahmed, 31000, Oran, Algeria

    Anes Moulai-Khatir

Authors
  1. Amira Fellous
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  2. Anes Moulai-Khatir
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  3. Moussadek Remili
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Fellous, A., Moulai-Khatir, A. & Remili, M. On stability and square integrability of solutions to some third order neutral differential equations. Afr. Mat. 33, 31 (2022). https://doi.org/10.1007/s13370-021-00936-z

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