We introduce some new oscillation criteria for a third-order linear differential equation with variable coefficients in this study. We found out the corollary as a result of the Storm comparison theory and used it to prove some theorems. Through it, we were able to achieve the necessary conditions for oscillation. We concluded that the solution to the differential equation is oscillating if it is bounded from below, and also if the discriminant of the equation is negative, its solution is oscillatory. We have given examples illustrating these results.
Cite this paper
Fthee, A. A. and Thanoon, T. Y. (2021). Conditions of Oscillation for a Linear Third-Order Differential Equation. Open Access Library Journal, 8, e7649. doi: http://dx.doi.org/10.4236/oalib.1107649.
Abdullah, H.K. (2004) A Note on the Oscillation of Second Order Differential Equations. Czechoslovak Mathematical Journal, 54, 949-954.
https://doi.org/10.1007/s10587-004-6443-3
Brtusek, M. (1999) On Oscillatory Solutions of Third Order Differential Equation with Quasiderivatives. Electronic Journal of Differential Equations, 3, 1-11.
Kim, R.J. (2011) Oscillation Criteria of Differential Equations of Second Order. Korean Journal of Mathematics, 19, 309-319.
https://doi.org/10.11568/kjm.2011.19.3.309
Aktas, M.F., Çakmak, D. and Tiryaki, A. (2011) On the Qualitative Behaviors of Solutions of Third Order Nonlinear Differential Equations. Computers & Mathematics with Applications, 62, 2029-2036.
https://doi.org/10.1016/j.camwa.2011.06.045
Aktas, M.F., Tiryaki, A. and Zafer, A. (2009) Integral Criteria for Oscillation of Third Order Nonlinear Differential Equations. Nonlinear Analysis: Theory, Methods & Applications, 71, e1496-e1502. https://doi.org/10.1016/j.na.2009.01.194
Cecchi, M., Doslá, Z. and Marini, M. (1997) Some Properties of Third Order Differential Operators. Czechoslovak Mathematical Journal, 47, 729-748.
https://doi.org/10.1023/A:1022878804065
Parhi, N. and Das, P. (1992) Oscillation Criteria for a Class of Nonlinear Differential Equations of Third Order. Annales Polonici Mathematici, 57, 219-229.
https://doi.org/10.4064/ap-57-3-219-229
Parhi, N. and Das, P. (1998) Oscillatory and Asymptotic Behaviour of a Class of Nonlinear Differential Equations of Third Order. Acta Mathematica Scientia, 18, 95-106. https://doi.org/10.1016/S0252-9602(17)30694-X
Parhi, N. and Das, P. (1998) On the Oscillation of a Class of Linear Homogeneous Third Order Differential Equations. Archivum Mathematicum, 34, 435-443.