Oscillation Criteria for First Order Neutral Differential Equations with Positive and Negative Coefficients

Sufficient conditions for the oscillation of the equation d xŽt. RŽt.xŽt r. dt PŽt.xŽt . QŽt.xŽt . 0, where P, Q, R CŽ t0 , ., R ., r Ž0, ., , R , , are obtained where RŽt. Ht t QŽu. du 1 is allowed to oscillate and the condition Ht 0s PŽs. QŽs . Hs PŽu. QŽu . du ds is not necessary. Some examples are given, which show that the results here are almost sharp.