ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

ACTA MATHEMATICA
UNIVERSITATIS COMENIANAE

Slowly varying solutions of a class of first order systems
of nonlinear differential equations

J. Jaroš and Takaŝi

Received: November 12, 2012; Accepted: February 6, 2013

Abstract. We analyze positive solutions of the two-dimensional systems of nonlinear differential equations

sustava

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 $t \to \infty$.

Keywords: systems of differential equations; positive solutions; asymptotic behavior; regularly varying functions.

AMS Subject classification: Primary: 34C11, 26A12

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Acta Mathematica Universitatis Comenianae
ISSN 0862-9544 (Printed edition)

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