Research Article

Oscillation criteria for solution to partial dynamic equations on time scales

Volume: 49 Number: 5 October 6, 2020
EN

Oscillation criteria for solution to partial dynamic equations on time scales

Abstract

We consider the oscillatory behavior of solutions to partial dynamic equation on time scales. We establish several oscillation criteria by applying a Ricatti transformation. Examples are provided to justify our results.

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Keywords

References

  1. [1] R.P. Agarwal, M. Bohner and S.H. Saker, Oscillation of second order delay dynamic equations, Can. Appl. Math. Q. 13, 1–18, 2005.
  2. [2] C.D. Ahlbrandt and C. Morian, Partial differential equations on time scales, J. Com- put. Appl. Math. 141, 35–55, 2002.
  3. [3] M. Bohner and G.S. Guseinov, Partial differentiation on time scales, Dynam. Systems Appl. 13, 351–379, 2004.
  4. [4] M. Bohner and A. Peterson, Dynamic Equations on Time Scale, An Introduction with Applications, Birkhäuser, Boston, 2001.
  5. [5] M. Bohner and S.H. Saker, Oscillation of second order nonlinear dynamic equations on time scales, Rocky Mountain J. Math. 34, 1239–1254, 2004.
  6. [6] M. Bohner, L. Erbe and A. Peterson, Oscillation for nonlinear second order dynamic equations on time scales, J. Math. Anal. Appl. 301, 491–507, 2005.
  7. [7] L. Erbe, A. Peterson and S.H. Saker, Oscillation criteria for second order nonlinear dynamic equations on time scales, J. Lond. Math. Soc. 67 (3), 701–714, 2003.
  8. [8] L.C. Evans, Partail Differential Equations, American Math. Society, Graduate Studies in Mathematics Vol. 19, second ed., 2010.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Publication Date

October 6, 2020

Submission Date

April 15, 2019

Acceptance Date

January 20, 2020

Published in Issue

Year 2020 Volume: 49 Number: 5

APA
Ramesh, R., Dıx, J. G., S, H., & Prakash, P. (2020). Oscillation criteria for solution to partial dynamic equations on time scales. Hacettepe Journal of Mathematics and Statistics, 49(5), 1788-1797. https://doi.org/10.15672/hujms.554157
AMA
1.Ramesh R, Dıx JG, S H, Prakash P. Oscillation criteria for solution to partial dynamic equations on time scales. Hacettepe Journal of Mathematics and Statistics. 2020;49(5):1788-1797. doi:10.15672/hujms.554157
Chicago
Ramesh, R., Julio G. Dıx, Harikrishnan S, and P. Prakash. 2020. “Oscillation Criteria for Solution to Partial Dynamic Equations on Time Scales”. Hacettepe Journal of Mathematics and Statistics 49 (5): 1788-97. https://doi.org/10.15672/hujms.554157.
EndNote
Ramesh R, Dıx JG, S H, Prakash P (October 1, 2020) Oscillation criteria for solution to partial dynamic equations on time scales. Hacettepe Journal of Mathematics and Statistics 49 5 1788–1797.
IEEE
[1]R. Ramesh, J. G. Dıx, H. S, and P. Prakash, “Oscillation criteria for solution to partial dynamic equations on time scales”, Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 5, pp. 1788–1797, Oct. 2020, doi: 10.15672/hujms.554157.
ISNAD
Ramesh, R. - Dıx, Julio G. - S, Harikrishnan - Prakash, P. “Oscillation Criteria for Solution to Partial Dynamic Equations on Time Scales”. Hacettepe Journal of Mathematics and Statistics 49/5 (October 1, 2020): 1788-1797. https://doi.org/10.15672/hujms.554157.
JAMA
1.Ramesh R, Dıx JG, S H, Prakash P. Oscillation criteria for solution to partial dynamic equations on time scales. Hacettepe Journal of Mathematics and Statistics. 2020;49:1788–1797.
MLA
Ramesh, R., et al. “Oscillation Criteria for Solution to Partial Dynamic Equations on Time Scales”. Hacettepe Journal of Mathematics and Statistics, vol. 49, no. 5, Oct. 2020, pp. 1788-97, doi:10.15672/hujms.554157.
Vancouver
1.R. Ramesh, Julio G. Dıx, Harikrishnan S, P. Prakash. Oscillation criteria for solution to partial dynamic equations on time scales. Hacettepe Journal of Mathematics and Statistics. 2020 Oct. 1;49(5):1788-97. doi:10.15672/hujms.554157

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