OSCILLATION CRITERIA FOR SECOND ORDER HALF-LINEAR DIFFERENTIAL EQUATIONS WITH DELAY

  • Radica Bojičić Faculty of Ekonomy, University of Priština, Kosovska Mitrovica
  • Tanja Jovanović Faculty of Natural Sciences and Mathematics, University of Priština, Kosovska Mitrovica
Keywords: Half-linear differential equations with delay, Oscillation criteria, Averaging function,

Abstract


The oscillation criteria of different types of differential equations are often the topic of numerous scientific papers, because their application in nuclear physics, fluid mechanics, relativistic mechanics, the study of chemical reactions in the system and in general are large in science. In this paper, the oscillation criteria using averaging functions of the half-linear differential equation are generalized to the half-linear differential equation with delay, under the appropriate assumptions for the delay function. Suitable examples illustrate the application of set oscillation criteria.

 

References

Bojičić, R. 2015. Oscillation properties of half-linear differential equation with delay. In Proceedings of the Sixth Mathematical Conference of the Republic of Srpska. in Serbian, pp. 122–134.

El-Sheikh, M., & Sallam, R. 2000. Oscillation criteria for second order functional differential equations. Applied Mathematics and Computation, 115(2-3), pp. 113-121.

Elbert, A. 1979. A half-linear second order differential equation. Colloquia Mathematica Societatis Janos Bolyai, 30, pp. 153-180.

Hardly, G., Littlewood, J., & Polya, G. 1988. Inequalities. Cambridge University.

Hsu, H., & Yeh, C. 1996. Oscillations theorems for second-order half-linear differential equations. Applied Mathematics Letters, 9(6), pp. 71-77.

Kusano, T., & Naito, Y. 1997. Oscillation and nonoscillation criteria for second-order quasilinear differential equations. Mathematica Hungarica, 76(1-2), pp. 81-99.

Kusano, T., & Wang, J. 1995. Oscillation properties of halflinear functional differential equation of the second order. Hiroshima Mathematical Journal, 25(2), pp. 371-385.

Li, H. J. 1995. Oscillation Criteria for Second Order Linear Differential Equations. Journal of Mathematical Analysis and Applications, 194(1), pp. 217-234. doi:10.1006/jmaa.1995.1295

Manojlović, J. V. 1999. Oscillation criteria for second-order half-linear differential equations. Mathematical and Computer Modelling, 30(5-6), pp. 109-119. doi:10.1016/s0895-7177(99)00151-x

Mirzov, J. 1976. On some analogs of Sturm's and Kneser's theorems for nonlinear systems. Journal of Mathematical Analysis and Applications, 53(2), pp. 418-425. doi:10.1016/0022-247x(76)90120-7

Philos, C. G. 1989. Oscillation theorems for linear differential equations of second order. Archiv der Mathematik, 53(5), pp. 482-492. doi:10.1007/bf01324723

Wang, J. 1997. Oscillation and nonoscillation theorems for a class of second order quasilinear functional-differential equations. Hiroshima Mathematical Journal, 27(3), pp. 449-466. doi:10.32917/hmj/1206126963

Published
2019/09/23
Section
Original Scientific Paper