X.H. Tang

New nonoscillation criteria for delay differential equations

Abstract This paper is concerned with the nonoscillation of first order delay differential equations of the form x′(t)+p(t)x τ(t) =0, t⩾t 0 , where p , τ ∈ C ([ t 0 ,∞), R + ), R + =[0,∞), τ ( t ) is nondecreasing, τ ( t ) t for t ⩾ t 0 and lim t →∞ τ ( t )=∞. New nonoscillation conditions are obtained. These conditions concern the case when the well-known nonoscillation condition ∫ τ(t) t p(s) ds⩽1/e is not satisfied.