New nonoscillation criteria for delay differential equations

This paper is concerned with the nonoscillation of first order delay differential equations of the form x′(t)+p(t)x<fen><cp type="lpar" STYLE="S">τ(t)<cp type="rpar" STYLE="S"></fen>=0, t&ges;t0, where <f>p,τ∈C([t0,∞),R+)</f>, <f>R+=[0,∞)</f>, <f>τ(t)</f> is nondecreasing, <f>τ(t)<t</f> for <f>t&ges;t0</f> and <f>limt→∞τ(t)=∞</f>. New nonoscillation conditions are obtained. These conditions concern the case when the well-known nonoscillation condition <f>∫τ(t)tp(s) ds&les;1/e</f> is not satisfied. [Copyright &y& Elsevier]