IJPAM: Volume 93, No. 2 (2014)

NEW OSCILLATION AND NON-OSCILLATION
CRITERIA FOR SECOND ORDER NONLINEAR
DIFFERENTIAL EQUATIONS

Xhevair Beqiri1, Elisabeta Koci2
1State University of Tetova
MACEDONIA
2University of Tirana
ALBANIA


Abstract. In this paper we have present new oscillation and non-oscillation criteria for nonlinear differential equations of second order with damping term

\begin{displaymath} (r(t)x'(t))'+p(t)x'(t)+q(t)f(g(x(t)))=0,\quad t\ge t_{0} >0 , \end{displaymath} (1)

where the coefficients are positive and continuous functions.

Also by using the generalized Riccati technique and positive function of Phillo we get a new oscillation and non-oscillation criteria for (1). The result is different from most known ones and improve some previous oscillation criteria and cover the cases which are not covered by known results.

Received: August 5, 2013

AMS Subject Classification: 34C10, 34C15

Key Words and Phrases: oscillation, non-oscillation, oscilation criteria, damping, second order equations

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DOI: 10.12732/ijpam.v93i2.1 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: 2014
Volume: 93
Issue: 2
Pages: 155 - 163

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