Language:   Search:   Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.

Query:
Fill in the form and click »Search«...
Format:
Display: entries per page entries
Zbl 1221.34245
Saker, S.H.; O'Regan, Donal
New oscillation criteria for second-order neutral functional dynamic equations via the generalized Riccati substitution.
(English)
[J] Commun. Nonlinear Sci. Numer. Simul. 16, No. 1, 423-434 (2011). ISSN 1007-5704

Summary: We establish some new sufficient conditions for oscillation of the second-order neutral functional dynamic equation $$(p(t)([y(t)+r(t)y(\tau(t))]^\Delta)^\gamma)^\Delta+f(t,y(\theta(t)))=0, ~t\in[t_0,\infty)_{\Bbb T}$$ on a time scale $\bbfT$, where $|f(t,u)|\ge q(t)|u^{\gamma }|$, $r, p$ and $q$ are real valued $rd$-continuous positive functions defined on $\bbfT$, $\gamma\ge 1$ is the quotient of odd positive integers. Our results improve previous existence results in the sense that our results do not require $p^{\Delta }(t)\ge0$, and $\int^{\infty}_{t_0}\theta^\gamma(s)q(s)[1-r(\theta(s))]^\gamma \Delta s=\infty$. Some examples are given to illustrate the main results.
MSC 2000:
*34N05
34K11 Oscillation theory of functional-differential equations
34K40 Neutral equations

Keywords: oscillation; second-order neutral dynamic equation; time scales

Highlights
Master Server