IJPAM: Volume 37, No. 4 (2007)

OSCILLATION CRITERIA FOR $n$-TH ORDER
NONLINEAR DIFFERENTIAL EQUATIONS
WITH DEVIATING ARGUMENT DEPENDING
ON THE UNKNOWN FUNCTION

N.T. Markova$^{1}$, P.S. Simeonov$^{2}$
$^{1}$ Technical University
Sliven, BULGARIA
$^{2}$ Medical University of Sofia
2 Dunav Str., Sofia, 1000, BULGARIA
e-mail: [email protected]


Abstract.In this paper differential equation of the type

\begin{displaymath} L_nx(t)+f(t,x(\Delta(t,x(t))))=0\eqno{\textrm{(E)}} \end{displaymath}

is considered, where $n\ge 2$ and the deviating argument $\Delta$ depends on the independent variable $t$ as well as on the unknown function $x$.

The oscillation of equation (E) is reduced to the oscillation of certain set of second order comparison differential equations.

Received: June 5, 2007

AMS Subject Classification: 34K15

Key Words and Phrases: oscillation criteria, nonlinear differential equations, deviating argument, second order comparison differential equations

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 37
Issue: 4