Geodesic
Slowly varying solutions of a class of first order systems of nonlinear differential equations
Acta mathematica Universitatis Comenianae, Tome 82 (2013) no. 2, pp. 265-284 
J. Jaroš; T. Kusano; J. Jaroš; T. Kusano. Slowly varying solutions of a class of first order systems of nonlinear differential equations. Acta mathematica Universitatis Comenianae, Tome 82 (2013) no. 2, pp. 265-284. http://geodesic.mathdoc.fr/item/AMUC_2013_82_2_a10/
@article{AMUC_2013_82_2_a10,
     author = {J. Jaro\v{s} and T. Kusano and J. Jaro\v{s} and T. Kusano},
     title = { Slowly varying solutions of a class of first order systems of nonlinear differential equations},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {265--284},
     year = {2013},
     volume = {82},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2013_82_2_a10/}
}
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We analyze positive solutions of the two-dimensional systems of nonlinear differential equations in the framework of regular variation and indicate the situation in which system (A) (resp. (B) possesses decaying solutions (resp. growing solutions) with precise asymptotic behavior as $t \to \infty$.