# Article

Full entry | PDF   (0.4 MB)
Keywords:
boundedness; stability; Liapunov function; differential equations of third order
Summary:
The paper studies the equation \begin{equation*}\dddot{X}+\Psi (\dot{X})\ddot{X}+\Phi (X)\dot{X}+cX=P(t) \end{equation*} in two cases: (i) $P(t)\equiv 0$, (ii) $P(t)\ne 0$. In case (i), the global asymptotic stability of the solution $X=0$ is studied; in case (ii), the boundedness of all solutions is proved.
References:
[1] Chukwu, E.N.: On boundedness of solutions of third ordr differential equations. Ann. Math. Pura Appl. (4) 104 (1975), 123–149. MR 0377180
[2] Ezeilo, J.O.C.: A generalization of a boundedness theorem for a certain third-order differential equation. Proc. Cambridge Philos. Soc. 63 (1967), 735–742. MR 0213657
[3] Liapunov, A.M.: Stability of Motion. Academic Press London, 1906. MR 0208093
[4] Mehri, B., Shadman, D.: Boundedness of solutions of certain third order differential equations. Math. Inequal. Appl. 2 (1999), no. 4, 545–549. MR 1717047
[5] Omeike, M.O., Afuwape, A.U.: New result on the ultimate boundedness of solutions of certain third-order vector differential equations. Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math. 49 (2010), no. 1, 55–61. MR 2797523
[6] Rao, M.R.M.: Ordinary Differential Equations. Affiliated East West Private Limited, London, 1980. Zbl 0482.34001
[7] Reissig, R., Sansone, G., Conti, R.: Nonlinear Differential Equations of Higher Order. Noordhoff Groningen, 1974.
[8] Tejumola, H.O.: A note on the boundedness and the stability of solutions of certain third order differential equations. Ann. Mat. Pura Appl. (4) 92 (1972), no. 4, 65–75. DOI 10.1007/BF02417936 | MR 0318615 | Zbl 0242.34046
[9] Tunc, C.: Uniform ultimate boundedness of the solutions of third order nonlinear differential equations. Kuwait J. Sci. Engrg. 12 (2005), no. 1, 39–48. MR 2145249 | Zbl 1207.34043
[10] Tunc, C.: On the stability and boundedness of solutions of nonlinear vector differential equations of third-order. Nonlinear Anal. 70 (2009), 2232–2236. DOI 10.1016/j.na.2008.03.002 | MR 2498299 | Zbl 1162.34043
[11] Tunc, C., Ates, M.: Stability and boundedness results for solutions of certain third order nonlinear vector differential equations. Nonlinear Dynam. 45 (2006), no. 3–4, 271–281. MR 2250136 | Zbl 1132.34328

Partner of