Have a personal or library account? Click to login
Stability and Square Integrability of Solutions to third order Neutral Delay Differential Equations Cover

Stability and Square Integrability of Solutions to third order Neutral Delay Differential Equations

Open Access
|Jan 2019

References

  1. [1] ADEMOLA, A. T.—ARAWOMO, P. O.: Uniform stability and boundedness of solutions of nonlinear delay differential equations of third order, Math. J. Okayama Univ. 55 (2013), 157–166.
  2. [2] BACULÍKOVÁ, B.—DŽURINA, J.: On the asymptotic behavior of a class of third order nonlinear neutral differential equations, Cent. Eur. J. Math. 8 (2010), 1091–1103.10.2478/s11533-010-0072-x
  3. [3] BARTUŠEK, M.—DOŠLÁ, Z.— GRAEF, J. R.: The Nonlinear Limit–Point/Limit–Circle Problem. Birkhäuser, Boston, 2004.10.1007/978-0-8176-8218-7
  4. [4] BARTUŠEK, M.— GRAEF, J. R.: The Strong Nonlinear Limit-Point/Limit-Circle Problem. In: Trends in Abstract and Applied Analysis, Vol. 6, World Scientific, Hackensack, NJ, 2018.10.1142/10608
  5. [5] _____On L2solutions of third order nonlinear differential equations, Dynam. Systems Appl. 9 (2000), 469–482.
  6. [6] _____Some limit-point/limit-circle results for third order differential equations, Discrete Contin. Dynam. Systems (2001), Suppl., 31–38.
  7. [7] BURTON, T. A.: Stability and Periodic Solutions of Ordinary and Functional Differential Equations. In: Math. Sci. Eng., Vol. 178, Academic Press, Orlando, 1985.
  8. [8] DOROCIAKOVÁ, B.: Some nonoscillatory properties of third order differential equations of neutral type, Tatra Mt. Math. Publ. 38 (2007), 71–76.
  9. [9] DOŠLÁ, Z.: On square integrable solutions of third order linear differential equations, in: Proc. of the Inter. Scientific Conf. Math., Herl’any, Slovakia, 1999 (A. Haščák, ed.), Univ. Technology Košice, 2000, pp. 68–72.
  10. [10] DOŠLÁ, Z.—LIŠKA, P.: Oscillation of third-order nonlinear neutral differential equations, Appl. Math. Lett. 56 (2016), 42–48.10.1016/j.aml.2015.12.010
  11. [11] _____Comparison theorems for third-order neutral differential equations, Electron. J. Differential Equations 2016 (2016), 1–13.
  12. [12] EZEILO, J. O. C.: On the stability of solutions of certain differential equations of the third order, Quart. J. Math. Oxford Ser. (2) 11 (1960), 64–69.10.1093/qmath/11.1.64
  13. [13] GRAEF, J. R.—BELDJERD, D.—REMILI, M.: On stability, ultimate boundedness, and existence of periodic solutions of certain third order differential equations with delay, Panamer. Math. J. 25 (2015), 82–94.
  14. [14] _____Stability and square integrability of solutions of nonlinear third order differential equations, Dyn. Contin. Discrete Impuls. Sys., Ser. A, Math. Anal. 22 (2015), 313–324.
  15. [15] GRAEF, J. R.—REMILI, M.: Asymptotic behavior of solutions of a third order nonlinear differential equation, Nonlinear Oscill. 20 (2017), 74–84.
  16. [16] _____Qualitative behavior of solutions of a third order nonlinear differential equation, Math. Nachr. 290 (2017), 2832–2844.10.1002/mana.201600491
  17. [17] GRAEF, J. R.—TUNÇ, C.: Global asymptotic stability and boundedness of certain multidelay functional differential equations of third order, Math. Methods Appl. Sci. 38 (2015), 3747–3752.10.1002/mma.3314
  18. [18] HADDOCK, J.: Stability theory for nonautonomous systems, in: An International Symposium, Providence, 1974, Dyn. Syst., Vol. 2, Academic Press, New York, 1976 pp. 271–274.10.1016/B978-0-12-164902-9.50057-5
  19. [19] HARA, T.: On the uniform ultimate boundedness of the solutions of certain third order differential equations, J. Math. Anal. Appl. 80 (1981), 533–544.10.1016/0022-247X(81)90122-0
  20. [20] MIHALÍKOVÁ, B.—KOSTIKOVÁ, E.: Boundedness and oscillation of third order neutral differential equations, Tatra Mt. Math. Publ. 43 (2009), 137–144.10.2478/v10127-009-0033-6
  21. [21] OMEIKE, M. O.: New results on the asymptotic behavior of a third-order nonlinear differential equation, Differ. Equ. Appl. 2 (2010), 39–51.10.7153/dea-02-04
  22. [22] OUDJEDI, L. D.—BELDJERD, O.—REMILI, M.: On the stability of solutions for non--autonomous delay differential equations of third-order, Differ. Uravn. Protsessy Upr. 2014 (2014), No. 1, 22–34.
  23. [23] PADHI, S.—PATI, S.: Theory of Third-Order Differential Equations. Springer, New Delhi, India, 2014.10.1007/978-81-322-1614-8
  24. [24] QIAN, C.: On global stability of third-order nonlinear differential equations, Nonlinear Anal. 42 (2000), 651–661.10.1016/S0362-546X(99)00120-0
  25. [25] REISSIG, R.—SANSONE, G.—CONTI, R.: Non-linear Differential Equations of Higher Order. In: Monogr. Textbooks Pure Appl. Math., Noordhoff Internat. Publ., Leyden, 1974.
  26. [26] OUDJEDI, L.—BELDJERD, D.—REMILI, M.: On the stability of solutions for non--autonomous delay differential equations of third-order, Differ. Uravn. Protsessy Upr. 2014 (2014), 22–34.
  27. [27] REMILI, M.—BELDJERD, D.: A boundedness and stability results for a kind of third order delay differential equations, Appl. Appl. Math. 10 (2015), 772–782.
  28. [28] _____On the asymptotic behavior of the solutions of third order delay differential equations, Rend. Circ. Mat. Palermo 63 (2014), 447–455.10.1007/s12215-014-0169-3
  29. [29] _____On ultimate boundedness and existence of periodic solutions of kind of third order delay differential equations, Acta Univ. M. Belii, Ser. Math. 24 (2016), 43–57.
  30. [30] _____Stability and ultimate boundedness of solutions of some third order differential equations with delay, J. Association Arab Univ. for Basic and Appl. Sci. 23 (2017), 90–95.10.1016/j.jaubas.2016.05.002
  31. [31] _____Boundedness and stability in third order nonlinear differential equations with bounded delay, An. Univ. Oradea Fasc. Mat. XXIII (2016), 135–143.
  32. [32] _____Boundedness and stability in third order nonlinear differential equations with multiple deviating arguments, Arch. Math. (Brno) 52 (2016), 79–90.10.5817/AM2016-2-79
  33. [33] _____Stability and boundedness of the solutions of non autonomous third order differential equations with delay, Acta Univ. Palack. Olomuc. Fac. Rerum. Natur. Math. 53 (2014), 139–147.
  34. [34] _____Stability of the solutions of nonlinear third order differential equations with multiple deviating arguments, Acta Univ. Sapientiae Math. 8 (2016), 150–165.10.1515/ausm-2016-0009
  35. [35] _____On asymptotic stability of solutions to third order nonlinear delay differential equation, Filomat 30 (2016),10.2298/FIL1612217R
  36. [36] _____Uniform stability and boundedness of a kind of third order delay differential equations, Bull. Comput. Appl. Math. 2 (2014), 25–35.
  37. [37] _____Uniform ultimate boundedness and asymptotic behaviour of third order nonlinear delay differential equation, Afr. Mat. 27 (2016), 1227–1237.10.1007/s13370-016-0405-4
  38. [38] REMILI, M.—OUDJEDI, L. D.—BELDJERD, D.: On the qualitative behaviors of solutions to a kind of nonlinear third order differential equation with delay, Comm. Appl. Anal. 20 (2016), 53–64.
  39. [39] 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. Difference Equ. 267 (2015), 14 p.10.1186/s13662-015-0604-6
  40. [40] TUNÇ, C.: Global stability of solutions of certain third-order nonlinear differential equations, Panamer. Math. J. 14 (2004), 31–35.
  41. [41] _____On the asymptotic behavior of solutions of certain third-order nonlinear differential equations, J. Appl. Math. Stoch. Anal. 1 (2005), 29–35.10.1155/JAMSA.2005.29
  42. [42] _____Boundedness of solutions of a third-order nonlinear differential equation, J. Inequal. Pure Appl. Math. 6 (2005), No. 1, Article 3, 6 p.
  43. [43] _____On the stability and boundedness of solutions to third order nonlinear differential equations with retarded argument, Nonlinear Dynam. 57 (2009), 97–106.10.1007/s11071-008-9423-6
  44. [44] _____Some stability and boundedness conditions for non-autonomous differential equations with deviating arguments, Elect. J. Qualitative Theory Diff. Equ. 2010 (2010), No. 1, 12 p.
  45. [45] _____The boundedness of solutions to nonlinear third order differential equations, Nonlinear Dyn. Syst. Theory 10 (2010), 97–102.
  46. [46] ZHANG, L.—YU, L.: Global asymptotic stability of certain third-order nonlinear differential equations, Math. Methods Appl. Sci. 36 (2013), 1845–1850.10.1002/mma.2729
DOI: https://doi.org/10.2478/tmmp-2018-0008 | Journal eISSN: 1338-9750 | Journal ISSN: 12103195
Language: English
Page range: 81 - 97
Submitted on: Mar 12, 2018
Published on: Jan 25, 2019
Published by: Slovak Academy of Sciences, Mathematical Institute
In partnership with: Paradigm Publishing Services
Publication frequency: 3 issues per year

© 2019 John R. Graef, Linda D. Oudjedi, Moussadek Remili, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.