Oscillation of nonlinear neutral delay differential equations of second-order with positive and negative coefficients

Authors

MUSTAFA KEMAL YILDIZ
BAŞAK KARPUZ
ÖZKAN ÖCALAN

DOI

10.3906/mat-0711-23

Abstract

Some oscillation criteria for the following second-order neutral differential equation [x(t)\pm r(t) f( x(t-\gamma))]''+p(t) g(x(t-\alpha)) -q(t) g(x(t-\beta )) = s(t) where t\geq t_0, \gamma,\alpha,\beta \in R^+ with \alpha \geq \beta, r \in C^2([t_0,\infty ), R^+) , p,q\in C([t_0,\infty ),R^+) and f,g\in C(R,R), s\in C([ t_0,\infty),R) have been obtained. Our results are not restricted with boundedness of solutions.

Keywords

Delay differential equations, neutral, nonlinear, oscillation, second-order.

First Page

341

Last Page

350

Recommended Citation

YILDIZ, MUSTAFA KEMAL; KARPUZ, BAŞAK; and ÖCALAN, ÖZKAN (2009) "Oscillation of nonlinear neutral delay differential equations of second-order with positive and negative coefficients," Turkish Journal of Mathematics: Vol. 33: No. 4, Article 4. https://doi.org/10.3906/mat-0711-23
Available at: https://journals.tubitak.gov.tr/math/vol33/iss4/4