Geodesic
Asymptotic behaviour of solutions of two-dimensional linear differential systems with deviating arguments
Archivum mathematicum, Tome 39 (2003) no. 3, pp. 213-232

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Sufficient conditions are established for the oscillation of proper solutions of the system \begin{align} u_1^{\prime }(t) =p(t)u_2(\sigma (t))\,, \\ u_2^{\prime }(t) =-q(t)u_1(\tau (t))\,, \end{align} where $p,\,q: R_{+}\rightarrow R_{+}$ are locally summable functions, while $\tau $ and $\sigma : R_{+}\rightarrow R_{+}$ are continuous and continuously differentiable functions, respectively, and $\lim \limits _{t\rightarrow +\infty } \tau (t)=+\infty $, $\lim \limits _{t\rightarrow +\infty } \sigma (t)=+\infty $.
Classification : 34K06, 34K11, 34K25
Keywords: two-dimensional differential system; proper solution; oscillatory system 
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     author = {Koplatadze, R. and Partsvania, N. L. and Stavroulakis, I. P.},
     title = {Asymptotic behaviour of solutions of two-dimensional linear differential systems with deviating arguments},
     journal = {Archivum mathematicum},
     pages = {213--232},
     publisher = {mathdoc},
     volume = {39},
     number = {3},
     year = {2003},
     mrnumber = {2010723},
     zbl = {1116.34331},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2003__39_3_a7/}
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Koplatadze, R.; Partsvania, N. L.; Stavroulakis, I. P. Asymptotic behaviour of solutions of two-dimensional linear differential systems with deviating arguments. Archivum mathematicum, Tome 39 (2003) no. 3, pp. 213-232. http://geodesic.mathdoc.fr/item/ARM_2003__39_3_a7/