On oscillation and asymptotic property of a class of third-order differential equations. (English) Zbl 0955.34023

The authors study oscillatory, nonoscillatory and some other questions on the asymptotic behaviour of solutions to the equation \[ y'''+a(t)y''+b(t)y'+c(t)y=0, \tag \(*\) \] with \(a\in C^2([\sigma ,+\infty [;\mathbb{R})\), \(b\in C^{'}([\sigma ,+\infty [;\mathbb{R})\), \(c\in C([\sigma ,+\infty [;\mathbb{R})\) and \(a(t)\leq 0\), \(b(t)\geq 0\), \(c(t)< 0\) for \(t\geq \sigma \). In particular, they establish several effective conditions for the existence of oscillatory solutions to \((*)\) and conditions guaranteeing nonoscillation of all solutions to \((*)\).


34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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[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. · Zbl 0167.07903
[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.
[3] M. Greguš: Third Order Linear Differential Equations. D. Reidel Pub. Co., Boston, 1987. · Zbl 0602.34005
[4] M. Hanan: Oscillation criteria for third-order linear differential equations. Pacific J. Math. 11 (1961), 919-944, MR 26 # 2695. · Zbl 0104.30901
[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
[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. · Zbl 0685.34032
[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. · Zbl 0803.34018
[8] N. Parhi, P. Das: On the oscillation of a class of linear homogeneous third order differential equations. To appear in Archivum Mathematicum. · Zbl 0973.34023
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