Sharp conditions for oscillations caused by delays

Abstract

AMS (MOS) subject classification (1970): Primary 34K15; Secondary 34K25, 34E10. A sufficient condition under which all solutions of the delay differential equation , where p(t≤0 and continuous and τ>0 and constant, are oscillatory is presented. It is explained that the condition is the best possible for oscillations. When the coefficient p(t) in equation (1) is a positive constant, p, then the condition becomes pτe>0 which is necessary and sufficient for all solutions of the DDE to be oscillatory.