IJPAM: Volume 54, No. 4 (2009)

OSCILLATORY BEHAVIOR OF THE SOLUTIONS OF
NONLINEAR $n$-TH ORDER DIFFERENTIAL EQUATIONS
WITH FORCING TERM AND RETARDED ARGUMENTS
DEPENDING ON THE UNKNOWN FUNCTION

N.T. Markova$^1$, P.S. Simeonov$^2$
$^1$Department of Mathematics, Physics and Chemistry
Technical University - Sliven
Sliven, 8800, BULGARIA
$^2$Faculty of Pharmacy
Medical University of Sofia
2, Dunav Str., Sofia, 1000, BULGARIA
e-mail: simeonov@pharmfac.net


Abstract.In this paper the $n$-th order differential equation

\begin{displaymath} L_n x(t) + f\left ( t, \tilde x \langle \Delta \left ( t,x(t) \right ) \rangle \right ) = q(t)\eqno{(E)} \end{displaymath}

is concidered, where $n \ge 2$ and the retarded arguments $\displaystyle \Delta= \left ( \Delta _1,\cdots ,\Delta _m \right )$ depend on the independent variable $t$ as well as on the unknown function $x$.

Some problems of the asymptotic and oscillatory behavior of the solutions of equation ($E$) are investigated.

Received: October 14, 2008

AMS Subject Classification: 34K15

Key Words and Phrases: asymptotic and oscillatory behavior, $n$-th order forced differential equations, retarded arguments depending on the unknown function

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 54
Issue: 4