Criteria of Oscillation for Second-Order Mixed Nonlinearities in Dynamic Equations
Abstract
:1. Introduction
2. Main Results
3. Results and Discussion
- (I)
- The results of this paper extend the Nehari-type oscillation criteria to the generalized mixed nonlinearities dynamic Equation (1) in all cases, and and on any arbitrary time scale, for all Also, in contrast to the previous literature, the results we have obtained in this work do not presume the fulfillment of condition (11).
- (II)
- The results can be applicable to all time scales, including with , with , and so forth (see [5]).
- (III)
- If , then criterion (19) reduces to
- (IV)
- It would be intriguing to apply the sharp Nehari-type criterion that the solutions of the second-order Euler differential equation are oscillatory when to a second-order dynamic equation, as demonstrated in [25].
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Hassan, T.S.; Iambor, L.F.; Mureşan, S.; Alenzi, K.; Odinaev, I.; Rashedi, K.A. Criteria of Oscillation for Second-Order Mixed Nonlinearities in Dynamic Equations. Symmetry 2024, 16, 1156. https://doi.org/10.3390/sym16091156
Hassan TS, Iambor LF, Mureşan S, Alenzi K, Odinaev I, Rashedi KA. Criteria of Oscillation for Second-Order Mixed Nonlinearities in Dynamic Equations. Symmetry. 2024; 16(9):1156. https://doi.org/10.3390/sym16091156
Chicago/Turabian StyleHassan, Taher S., Loredana Florentina Iambor, Sorin Mureşan, Khalid Alenzi, Ismoil Odinaev, and Khudhayr A. Rashedi. 2024. "Criteria of Oscillation for Second-Order Mixed Nonlinearities in Dynamic Equations" Symmetry 16, no. 9: 1156. https://doi.org/10.3390/sym16091156