# Article

 Title: On oscillation and asymptotic property of a class of third order differential equations (English) Author: Parhi, N. Author: Pardi, Seshadev Language: English Journal: Czechoslovak Mathematical Journal ISSN: 0011-4642 (print) ISSN: 1572-9141 (online) Volume: 49 Issue: 1 Year: 1999 Pages: 21-33 Summary lang: English . Category: math . Summary: In this paper, oscillation and asymptotic behaviour of solutions of $y^{\prime \prime \prime } + a(t)y^{\prime \prime }+b(t)y^{\prime } + c(t)y=0$ have been studied under suitable assumptions on the coefficient functions $a,b,c\in C([\sigma ,\infty ),R)$, $\sigma \in R$, such that $a(t)\ge 0$, $b(t) \le 0$ and $c(t) < 0$. (English) MSC: 34C10 idZBL: Zbl 0955.34023 idMR: MR1676698 . Date available: 2009-09-24T10:19:25Z Last updated: 2020-07-03 Stable URL: http://hdl.handle.net/10338.dmlcz/127463 . Reference: [1] S. Ahmad, A.C. Lazer: On the oscillatory behaviour of a class of linear third order differential equations.J. Math. Anal. Appl. 28 (1970), 681–689, MR 40 # 1646. MR 0248394 Reference: [2] M. Gera: On the behaviour of solutions of the differential equation $x^{\prime \prime \prime }+a(t) x^{\prime \prime }+b(t) x^{\prime }+c(t) x =0$.Habilitation Thesis, Faculty of Mathematics and Physics, Comenius University, Bratislava. (Slovak) Reference: [3] M. Greguš: Third Order Linear Differential Equations.D. Reidel Pub. Co., Boston, 1987. MR 0882545 Reference: [4] M. Hanan: Oscillation criteria for third-order linear differential equations.Pacific J. Math. 11 (1961), 919–944, MR 26 # 2695. Zbl 0104.30901, MR 0145160 Reference: [5] G.D. Jones: Properties of solutions of a class of third order differential equations.J. Math. Anal. Appl. 48 (1974), 165–169. Zbl 0289.34046, MR 0352608, 10.1016/0022-247X(74)90224-8 Reference: [6] N. Parhi, S. Parhi: Qualitative behaviour of solutions of forced nonlinear third order differential equations.Rivista di Matematica della Universita di Parma 13 (1987), 201–210. MR 0977675 Reference: [7] N. Parhi, P. Das: On asymptotic property of solutions of linear homogeneous third order differential equations.Bollettino U.M.I 7-B (1993), 775–786. MR 1255647 Reference: [8] N. Parhi, P. Das: On the oscillation of a class of linear homogeneous third order differential equations.To appear in Archivum Mathematicum. MR 1679638 .

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