ON ASYMPTOTIC BEHAVIOR OFSOLUTIONS OF n-TH ORDER EMDEN-FOWLER DIFFERENTIAL EQUATIONS WITH ADVANCED ARGUMENT

We study oscillatory properties of solutions of the Emden-Fowler type differential equation u((n))(t)+p(t)|u(sigma(t))|(lambda) sign u(sigma(t))=0, where 0 < lambda < 1, p is an element of L-loc (R+;R), sigma is an element of C(R+;R+) and sigma(t)>= t for t is an element of R+. Sufficient (necessary and sufficient) conditions of new type for oscillation of solutions of the above equation are established. Some results given in this paper generalize the results obtained in the paper by Kiguradze and Stavroulakis (1998).