Article
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 $c(t) < 0$.
References:
[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
[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)
[3] M. Greguš:
Third Order Linear Differential Equations. D. Reidel Pub. Co., Boston, 1987.
MR 0882545
[4] M. Hanan:
Oscillation criteria for third-order linear differential equations. Pacific J. Math. 11 (1961), 919–944, MR 26 # 2695.
MR 0145160 |
Zbl 0104.30901
[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
[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
[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