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Slowly Varying Solutions of a Class of First Order Systems of Nonlinear Differential Equations

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Author(s): J. Jaroš | Takaŝi

Journal: Acta Mathematica Universitatis Comenianae
ISSN 0862-9544

Volume: LXXXII;
Issue: 2;
Start page: 265;
Date: 2013;
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Keywords: systems of differential equations | positive solutions | asymptotic behavior | regularly varying functions

ABSTRACT
We analyze positive solutions of the two-dimensional systems of nonlinear differential equations egin{gather} x' + p(t)y^{alpha} = 0, qquad y' + q(t)x^{eta} = 0, ag{A}%label{a} \ x' = p(t)y^{alpha}, qquad y' = q(t)x^{eta}, ag{B}%label{b}end{gather}%% in the framework of regular variation and indicate the situation in which system eqref{a} (resp. eqref{b}) possesses decaying solutions (resp. growing solutions) with precise asymptotic behavior as $t o infty$.
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