Oscillation Theorems for Non-liner Delay Differential Equations

Abstract

First, an oscillation theorem is presented for the n-th order delay differential equation\[ (r(t)x'(t))(n-1)+∑k_{i=1}fi(t)Fi(xτ_i(t), x'τ_i(t), ..., x(n-1)τ_i(t))=b(t), \ \ r(t)>0.\]Then the asymptotic behavior of bounded oscillatory solutions of the above equations is investigated.