IJPAM: Volume 64, No. 2 (2010)

OSCILLATION CRITERIA FOR $n$-TH ORDER
NONLINEAR DIFFERENTIAL EQUATIONS
WITH ``MAXIMA"

D. Kolev$^1$, N. Markova$^2$, S. Nenov$^3$
$^{1,3}$Department of Mathematics
University of Chemical Technology and Metallurgy
8, Kliment Ohridski Blvd., Sofia, 1756, BULGARIA
$^1$e-mails: [email protected], [email protected]
$^3$e-mails: [email protected]
$^2$Department of Mathematics, Physics and Chemistry
Technical University of Sofia, Branch of Sliven
Sliven, 8800, BULGARIA
e-mail: n markova [email protected]


Abstract.In this paper differential equations with ``maxima'' of the type

\begin{displaymath}
L_n x(t)+f(t,\max _{[\sigma (t),\tau (t)]} x(s))=0\eqno{(E)}
\end{displaymath}

is considered, where $n\ge 2$, $\sigma (t),\tau (t)$ are continuous functions and $\sigma (t)\le \tau (t)\le t$.

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

Received: September 1, 2009

AMS Subject Classification: 34K15

Key Words and Phrases: oscillation criteria, nonlinear differential equations, ``maxima'', second order comparison differential equations

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 64
Issue: 2