Oscillation of odd order neutral differential equations

Abstract

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Oscillation of odd order neutral delay differential equation

“…x'(t) +x(t) = 0 are nonoscillatory. The results of this paper was motivated by certain recent results due to Gopalsamy, et al [3], Graef et al [4] and Zhang [8].…”

“…which by Theorem 2.2 [3] implies that Eq. (1) has a nonoscillatory solution, a contradiction to our assumption.…”

“…t=i Consequently, by Theorem 2.2 of [3] and the remark following it, we see that the equation associated with (15), that is, Eq. (3) admits a nonoscillatory solution, which again is a contradiction to our assumption.…”

“…In [3], authors proved that if (Ci) Q € C([a,oo),lR + ), IR + = (0,oc), r,OG (0,oo), pG[0,l) then every solution of the odd order neutral delay differential equation…”

“…Hence every solution of it oscillates. Theorem 4.1 due to Gopalsamy, et al [3] is not applicable to it.…”