Displaying similar documents to “Oscillation criteria for functional differential equations.”

On property (B) of higher order delay differential equations

Blanka Baculíková, Jozef Džurina (2012)

Archivum Mathematicum

Similarity:

In this paper we offer criteria for property (B) and additional asymptotic behavior of solutions of the n -th order delay differential equations ( r ( t ) [ x ( n - 1 ) ( t ) ] γ ) ' = q ( t ) f ( x ( τ ( t ) ) ) . 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 r - 1 / γ ( t ) t = and r - 1 / γ ( t ) t < are discussed. ...