Geodesic
An Oscillation Criterion for First Order Linear Delay Differential Equations
Canadian mathematical bulletin, Tome 41 (1998) no. 2, pp. 207-213

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DOI

A new oscillation criterion is given for the delay differential equation ${x}'\,(t)\,+\,p(t)x\,(t\,-\,\text{ }\!\!\tau\!\!\text{ (t)})\,=\,0$ , where $p,\,\text{ }\!\!\tau\!\!\text{ }\,\in \,\text{C}\,\text{( }\!\![\!\!\text{ 0,}\,\infty ),\,\text{ }\!\![\!\!\text{ 0,}\,\infty )\text{)}$ and the function $T$ defined by $T(t)\,=\,t-\,\text{ }\!\!\tau\!\!\text{ }\,\text{(t),}\,\text{t}\ge \,\text{0}$ is increasing and such that ${{\lim }_{t\to \infty }}\,T(t)\,=\,\infty $ . This criterion concerns the case where $\lim \,{{\inf }_{t\to \infty }}\int _{T(t)}^{t}p(s)ds\le \frac{1}{e}$ .
DOI : 10.4153/CMB-1998-030-3
Mots-clés : 34K15, Delay differential equation, oscillation 
Philos, CH. G.; Sficas, Y. G. An Oscillation Criterion for First Order Linear Delay Differential Equations. Canadian mathematical bulletin, Tome 41 (1998) no. 2, pp. 207-213. doi: 10.4153/CMB-1998-030-3
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     author = {Philos, CH. G. and Sficas, Y. G.},
     title = {An {Oscillation} {Criterion} for {First} {Order} {Linear} {Delay} {Differential} {Equations}},
     journal = {Canadian mathematical bulletin},
     pages = {207--213},
     year = {1998},
     volume = {41},
     number = {2},
     doi = {10.4153/CMB-1998-030-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1998-030-3/}
}
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