Startseite Oscillation results for second-order mixed neutral differential equations with distributed deviating arguments
Artikel
Lizenziert
Nicht lizenziert Erfordert eine Authentifizierung

Oscillation results for second-order mixed neutral differential equations with distributed deviating arguments

  • Chenghui Zhang EMAIL logo , Blanka Baculíková , Jozef Džurina und Tongxing Li
Veröffentlicht/Copyright: 25. August 2016
Veröffentlichen auch Sie bei De Gruyter Brill

Abstract

We obtain some oscillation criteria for all solutions to a second-order mixed neutral differential equation with distributed deviating arguments. The results presented improve those reported in the literature.

MSC 2010: Primary 34C10; 34K11

This research is supported by the National Key Basic Research Program of P. R. China (2013CB035604) and the NNSF of P. R. China (Grant Nos. 61034007, 51277116, 51107069)



(Communicated by Michal Fečkan)


Acknowledgement

The authors would like to thank Professor Michal Fečkan and the anonymous referees for their thoughtful review of this manuscript and their insightful comments used to improve the quality of this paper.

References

[1] Baculíková, B.: Oscillation criteria for second order nonlinear differential equations, Arch. Math. (Brno) 42 (2006), 141–149.Suche in Google Scholar

[2] Baculíková, B.—Džurina, J.—Li, T.: Oscillation results for even-order quasilinear neutral functional differential equations, Electron. J. Differential Equations 2011 (2011), 1–9.10.14232/ejqtde.2011.1.74Suche in Google Scholar

[3] Baculíková, B.—Li, T.—Džurina, J.: Oscillation theorems for second-order superlinear neutral differential equations, Math. Slovaca 63 (2013), 123–134.10.2478/s12175-012-0087-9Suche in Google Scholar

[4] Candan, T.: Oscillation of solutions for odd-order neutral functional differential equations, Electron. J. Differential Equations 2010 (2010), 1–10.10.1155/2010/184180Suche in Google Scholar

[5] Candan, T.: Oscillation behavior of solutions for even order neutral functional differential equations, Appl. Math. Mech. (English Ed.) 27 (2006), 1311–1320.10.1007/s10483-006-1003-1Suche in Google Scholar

[6] Candan, T.—Dahiya, R. S.: Oscillation of mixed neutral functional differential equations with distributed deviating arguments, Differ. Equ. Dyn. Syst. 16 (2008), 207–223.10.1007/s12591-008-0013-3Suche in Google Scholar

[7] Candan, T.—Dahiya, R. S.: On the oscillation of certain mixed neutral equations, Appl. Math. Lett. 21 (2008), 222–226.10.1016/j.aml.2007.02.021Suche in Google Scholar

[8] Džurina, J.—Busa, J.—Airyan, E. A.: Oscillation criteria for second-order differential equations of neutral type with mixed arguments, Differ. Equ. 38 (2002), 137–140.10.1023/A:1014872030186Suche in Google Scholar

[9] Džurina, J.—Hudáková, D.: Oscillation of second order neutral delay differential equations, Math. Bohem. 134 (2009), 31–38.10.21136/MB.2009.140637Suche in Google Scholar

[10] Grace, S. R.: On the oscillations of mixed neutral equations, J. Math. Anal. Appl. 194 (1995), 377–388.10.1006/jmaa.1995.1306Suche in Google Scholar

[11] Hasanbulli, M.—Rogovchenko, Yu. V.: Oscillation criteria for second order nonlinear neutral differential equations, Appl. Math. Comput. 215 (2010), 4392–4399.10.1016/j.amc.2010.01.001Suche in Google Scholar

[12] Hasanbulli, M.—Rogovchenko, Yu. V.: Asymptotic behavior of nonoscillatory solutions to n-th order nonlinear neutral differential equations, Nonlinear Anal. 69 (2008), 1208–1218.10.1016/j.na.2007.06.025Suche in Google Scholar

[13] Li, T.: Comparison theorems for second-order neutral differential equations of mixed type, Electron. J. Differential Equations 2010 (2010), 1–7.10.1155/2010/215856Suche in Google Scholar

[14] Li, T.—Agarwal, R. P.—Bohner, M.: Some oscillation results for second-order neutral differential equations, J. Indian Math. Soc. 79 (2012), 97–106.Suche in Google Scholar

[15] Li, T.—Baculíková, B.—Džurina, J.: Oscillation results for second-order neutral differential equations of mixed type, Tatra Mt. Math. Publ. 48 (2011), 101–116.10.2478/v10127-011-0010-8Suche in Google Scholar

[16] Li, T.—Han, Z.—Zhang, C.—Li, H.: Oscillation criteria for second-order superlinear neutral differential equations, Abstr. Appl. Anal. 2011 (2011), 1–17.10.1155/2011/328914Suche in Google Scholar

[17] Li, T.—Han, Z.—Zhao, P.—Sun, S.: Oscillation of even-order neutral delay differential equations, Adv. Difference Equ. 2010 (2010), 1–9.10.1155/2010/727486Suche in Google Scholar

[18] Li, T.—Rogovchenko, Yu. V.—Zhang, C.: Oscillation of second-order neutral differential equations, Funkcial. Ekvac. 56 (2013), 111–120.10.1619/fesi.56.111Suche in Google Scholar

[19] Li, T.—Şenel, M. T.—Zhang, C.: Oscillation of solutions to second-order half-linear differential equations with neutral terms, Electron. J. Differential Equations 2013 (2013), 1–7.10.1155/2013/802324Suche in Google Scholar

[20] Qi, Y.—Yu, J.: Oscillation of second order nonlinear mixed neutral differential equations with distributed deviating arguments, Bull. Malays. Math. Sci. Soc. (2) 38 (2015), 543–560.10.1007/s40840-014-0035-7Suche in Google Scholar

[21] Thandapani, E.—Piramanantham, V.: Oscillation criteria of second order neutral delay dynamic equations with distributed deviating arguments, Electron. J. Qual. Theory Differ. Equ. 2010 (2010), 1–15.10.14232/ejqtde.2010.1.61Suche in Google Scholar

[22] Wang, P. G.: Oscillation criteria for second order neutral equations with distributed deviating arguments, Comput. Math. Appl. 47 (2004), 1935–1946.10.1016/j.camwa.2002.10.016Suche in Google Scholar

[23] Wang, P. G.—Teo, K. L.—Liu, Y. Q.: Oscillation properties for even order neutral equations with distributed deviating arguments, J. Comput. Appl. Math. 182 (2005), 290–303.10.1016/j.cam.2004.12.010Suche in Google Scholar

[24] Xu, Z. T.—Weng, P. X.: Oscillation of second-order neutral equations with distributed deviating arguments, J. Comput. Appl. Math. 202 (2007), 460–477.10.1016/j.cam.2006.03.001Suche in Google Scholar

[25] Yan, J. R.: Oscillation of higher order neutral differential equations, J. Austral. Math. Soc. Ser. A 64 (1998), 73–81.10.1017/S1446788700001300Suche in Google Scholar

[26] Yu, Y. H.—Fu, X. L.: Oscillation of second order neutral equation with continuous distributed deviating argument, Rad. Mat. 7 (1991), 167–176.Suche in Google Scholar

[27] Zhang, C.—Şenel, M. T.—Li, T.: Oscillation of second-order half-linear differential equations with several neutral terms, J. Appl. Math. Comput. 44 (2014), 511–518.10.1007/s12190-013-0705-xSuche in Google Scholar

[28] Zhao, J. H.—Meng, F. W.: Oscillation criteria for second-order neutral equations with distributed deviating argument, Appl. Math. Comput. 206 (2008), 485–493.10.1016/j.amc.2008.09.021Suche in Google Scholar

Received: 2013-3-20
Accepted: 2013-11-29
Published Online: 2016-8-25
Published in Print: 2016-6-1

© 2016 Mathematical Institute Slovak Academy of Sciences

Artikel in diesem Heft

  1. Research Article
  2. On the vertex-to-edge duality between the Cayley graph and the coset geometry of von Dyck groups
  3. Research Article
  4. Characterization of hereditarily reversible posets
  5. Research Article
  6. Families of sets which can be represented as sublattices of the lattice of convex subsets of a linearly ordered set
  7. Research Article
  8. Diophantine equation X4+Y4 = 2(U4 + V4)
  9. Research Article
  10. On the congruent number problem over integers of cyclic number fields
  11. Research Article
  12. On the Diophantine equation x2 + C= yn for C = 2a3b17c and C = 2a13b17c
  13. Research Article
  14. Representations and evaluations of the error term in a certain divisor problem
  15. Research Article
  16. A construction of a Peano curve
  17. Research Article
  18. Compositions of ϱ-upper continuous functions
  19. Research Article
  20. Products of Świa̧tkowski functions
  21. Research Article
  22. Subclasses of meromorphically p-valent functions involving a certain linear operator
  23. Research Article
  24. Oscillation results for second-order mixed neutral differential equations with distributed deviating arguments
  25. Research Article
  26. Oscillation criteria for higher order nonlinear delay dynamic equations on time scales
  27. Research Article
  28. On the solutions of a fourth order parabolic equation modeling epitaxial thin film growth
  29. Research Article
  30. Meromorphic solutions of q-shift difference equations
  31. Research Article
  32. Oscillation criteria for higher-order nonlinear delay dynamic equations on time scales
  33. Research Article
  34. Multiplier spaces and the summing operator for series
  35. Research Article
  36. Weighted αβ-statistical convergence of Kantorovich-Mittag-Leffler operators
  37. Research Article
  38. The local spectral radius of a nonnegative orbit of compact linear operators
  39. Research Article
  40. A note on Lie product preserving maps on Mn(ℝ)
  41. Research Article
  42. On vector optimality conditions for constrained problems with -stable data
  43. Research Article
  44. Reparameterization of weakly nonlinear regression models with constraints
  45. Research Article
  46. Convolutions of polynomial kernels
  47. Research Article
  48. Closed form evaluation of sums containing squares of Fibonomial coefficients
Heruntergeladen am 4.11.2025 von https://www.degruyterbrill.com/document/doi/10.1515/ms-2015-0165/html?lang=de
Button zum nach oben scrollen