In this paper I study the oscillatory behaviour of equations
(*) yi(t)+qy(t)+±17 piy(t- ri).0 and (**)yi(t)-gy(t) -
i=1 i=1
where q?, 0, pi> 0 and ti 0, are constants, i=1, ,n. It
each of the following conditions (1)pit exp(14-q ti) > 1 fo
, n, (2) ( l pi) exp (1+q )2- >1, where = min Iry t2,
A
*Military Techinical College, Cairo. Egypt. Department of MatheMatics .
of the forms p.y(t+r.1 )=Ds
is proved that r some i,1=1,2,
../tn),(3)
t(17p.)( S. )exp(n+q ti) 1, or (4) CZ' (q/n+ . ) j i > e implies
iri i i i pi
i T12 2 n implies
i=1 i=1
that every solution of (*) or (**) oscillates. A generalization in the
case where the coefficients q>, 0, pi) 0 1=1,...,n are continuous functions of t is also presented.