On proper oscillatory solutions of the nonlinear differential equations of the -th order
In this paper we offer criteria for property (B) and additional asymptotic behavior of solutions of the -th order delay differential equations Obtained results essentially use new comparison theorems, that permit to reduce the problem of the oscillation of the n-th order equation to the the oscillation of a set of certain the first order equations. So that established comparison principles essentially simplify the examination of studied equations. Both cases and are discussed.
Integral criteria are established for and , where is the space of solutions of the equation satisfying the condition