Oscillation of third order functional differential equations with delay. (English) Zbl 1028.34061

Candan, Tuncay; Dahiya, Rajbir S.

Electron. J. Differ. Equ. 2003, Conf. 10, 79-88 (2003).

From the introduction: Our goal here is to study functional-differential equations of the form \[ (b(t)(a(t) x'(t))')'+ \sum^m_{i=1} q_i(t) f(x(\sigma_i(t)))= h(t), \] where \(a,b,h\in C([t_0, \infty)\mathbb{R})\), \(a(t),b(t)> 0\), \(f:\mathbb{R}\to \mathbb{R}\) continuous, \(\sigma_i(t)\to \infty\), as \(t\to\infty\), \(i= 1,2,\dots, m\), and \[ (b(t) (a(t) x'(t))')'+ \int^d_c q(t,\xi) f(x(\sigma(t, \xi))) d\xi= 0, \] with \(a,b\in C([t_0, \infty),\mathbb{R})\), \(f\in C(\mathbb{R},\mathbb{R})\).

MSC:

34K11

Oscillation theory of functional-differential equations

Keywords:

oscillation theory