Symmetry and Its Role in Oscillation of Solutions of Third-Order Differential Equations
Abstract
:1. Introduction
2. Main Results
- ()
- , , , and , or
- ()
- , , , and .
- (1)
- . From , there exists a constant , such that
- (2)
- . From (14), there exists a constant and , such thatHence,
- ()
- for and for ,
- ()
- , and some locally integrable function , such that
3. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Acknowledgments
Conflicts of Interest
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Kumar, M.S.; Bazighifan, O.; Al-Shaqsi, K.; Wannalookkhee, F.; Nonlaopon, K. Symmetry and Its Role in Oscillation of Solutions of Third-Order Differential Equations. Symmetry 2021, 13, 1485. https://doi.org/10.3390/sym13081485
Kumar MS, Bazighifan O, Al-Shaqsi K, Wannalookkhee F, Nonlaopon K. Symmetry and Its Role in Oscillation of Solutions of Third-Order Differential Equations. Symmetry. 2021; 13(8):1485. https://doi.org/10.3390/sym13081485
Chicago/Turabian StyleKumar, M. Sathish, Omar Bazighifan, Khalifa Al-Shaqsi, Fongchan Wannalookkhee, and Kamsing Nonlaopon. 2021. "Symmetry and Its Role in Oscillation of Solutions of Third-Order Differential Equations" Symmetry 13, no. 8: 1485. https://doi.org/10.3390/sym13081485
APA StyleKumar, M. S., Bazighifan, O., Al-Shaqsi, K., Wannalookkhee, F., & Nonlaopon, K. (2021). Symmetry and Its Role in Oscillation of Solutions of Third-Order Differential Equations. Symmetry, 13(8), 1485. https://doi.org/10.3390/sym13081485