Oscillation Criteria for a Class of Second Order Neutral Delay Differential Equations

Abstract

Abstract:Oscillation criteria for a class of second order neutral delay differential equations of the form + − ′ ′+ − =0, ≥ 0 is studied. By using first and second mean value theorem of integrals, the new sufficient condition is obtained and the corresponding result what was already obtained is generalized by the result in this paper.

Qualitative properties of certain non-linear differential systems of second order

“…The study of qualitative behaviors of solutions, asymptotic behavior, stability, instability, boundedness, convergence, square integrability, etc., to differential equations of second order seems to be an important problem of the qualitative differential equations theory and has both theoretical and practical values in the literature. Numerous works were done on the subject (for example, see, the books or the papers of Ahmad and Rama Mohana Rao [1], El-Sheikh et al [2], Gallot et al [3], Grigoryan [4], Gu and Yu [5], Korkmaz and Tunc [6], Kroopnick [7], Pettini and Valdettaro [8], Kulcsar [11], Ogundare et al [12], Sanchez [13], Shi [14], Tunc [15][16][17][18], Tunc and Tunc [19,20], Zhao [21] and the cited papers or books therein). However, we would not like to give here the details of the works and applications done regarding the mentioned qualitative properties.…”