×

zbMATH — the first resource for mathematics

On the non-oscillation of solutions of some nonlinear differential equations of third order. (English) Zbl 1140.34415
From the introduction: We are concerned with non-oscillation of solutions of third-order nonlinear differential equations of the form
\[ (r(t)y''(t))' + q(t)y'(t) +p(t)y^\alpha(g(t)) = f(t),\quad t\geq t_0,\tag{1} \]
and
\[ (r(t)y''(t))' + q(t) (y'(g_1(t)))^\beta+p(t)y^\alpha(g(t)) = f(t),\quad t\geq t_0,\tag{2} \]
where \(t_0\geq 0\) is a fixed real number, \(f\), \(p\), \(q\), \(r\), \(g\) and \(g_1\in C([0,\infty),{\mathbb R})\) such that \(r(t) > 0\) and \(f(t)\geq 0\) forall \(t\in [0,\infty)\). Throughout the paper, it is assumed, for all \(g(t)\), \(g_1(t)\), \(\alpha\) and \(\beta\) appeared in (1) or (2), that \(g(t)\leq t\) and \(g_1(t)\leq t\) for all \(t\geq t_0\); \(\lim_{t\to\infty}g(t) = \infty\) and \(\lim_{t\to\infty}g_1(t) = \infty\); both \(\alpha > 0\) and \(\beta > 0\) are quotients of odd integers.

MSC:
34K11 Oscillation theory of functional-differential equations
PDF BibTeX XML Cite