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Asymptotic behaviour of solutions of two-dimensional linear differential systems with deviating arguments
Archivum mathematicum, Tome 39 (2003) no. 3, pp. 213-232 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $.
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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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/

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