IJPAM: Volume 103, No. 3 (2015)

NEW OSCILLATION CRITERIA FOR SECOND ORDER
NONLINEAR DIFFERENTIAL EQUATIONS

Xhevair Beqiri$^1$, Azir Jusufi$^2$
$^{1,2}$Department of Mathematics
State university of Tetova
1200, Tetova, REPUBLIC OF MACEDONIA


Abstract. In this paper we present criteria for oscillation of nonlinear differential equations of second order

\begin{displaymath}
(a(t)u'(t))'+p(t)f(u(g(t))=0 ,
\end{displaymath} (1)

where the coefficient a(t) is nonnegative, continuous function and $f(x)$, $g(x)$ are continuous functions which complete certain conditions.

Here we use generalized Riccati technique and the conclusion is also based on building functions where there are involved coefficients of equation ([*]) and also Philos functions $H(t,s)>0$.

This criteria is based on the results of Blanka Bakulikova and get argumentum with the example in the end of this work paper.

Received: June 20, 2015

AMS Subject Classification: 34C10, 34C15

Key Words and Phrases: oscillation, differential equation, second order, interval, relation etc

Download paper from here.




DOI: 10.12732/ijpam.v103i3.16 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 103
Issue: 3
Pages: 557 - 565


Google Scholar; DOI (International DOI Foundation); WorldCAT.

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).