Oscillation criteria for delay equations

Abstract

Abstract. This paper is concerned with the oscillatory behavior of first-order delay differential equations of the form

New Oscillation Ciriteria of First Order Delay Differential Equations

“…(l.l) and (1.2) recpectivelly. Then our results improve the results of [13], [17] and [9], and simply for verification throughout examples than of the results in [7], [4], [14], [11] and [12],…”

“…(l.l) when the limit, t lim ( P(s)ds t-• 00 J t-T does not exist. How to fill this gap is an interesting problem which has been recently investigated by several authors (see [7], [4], [14], [11] and [12]). They have established some new finite sufficient conditions for oscillation of all solutions of Eq.…”

“…(l.l) which extended and improved the conditions (1.3) and (1.4). The techniques that are used in [7], [4], [14], [11] and [12] are not applied to Eq. (1.2) to fill the gap between (1.5) and (1.6).…”

Oscillation of first order delay differential equations with distributed delay

“…In the recent literature, there have been numerous results on the oscillation for delay differential equation with discrete delays; see, for example, papers [1,4,[8][9][10][11][12][13][14][15][17][18][19][20][21][22][23], books [5,7,16] and references therein. But only a relatively few publications on oscillation for delay differential equation with distributed delay are found; see [2,3] and references cited ✩ This work was supported by NNSF of China.…”

“…Integral conditions like (1.4) and (1.5) have been employed extensively in the study of the oscillatory properties of various functional differential equations. When the limit lim t →∞ t t −τ p(s) ds does not exist, there is an obvious gap between 1/e and 1; in the recent literature [9,11,[16][17][18][19][20][21] …”