p. 265 - 284 Slowly varying solutions of a class of first order systems of nonlinear differential equations J. Jaroš and Takaŝi Kusano Received: November 12, 2012; Accepted: February 6, 2013 Abstract. 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 $t \to \infty$. Keywords: systems of differential equations; positive solutions; asymptotic behavior; regularly varying functions. AMS Subject classification: Primary: 34C11, 26A12 PDF Compressed Postscript Version to read ISSN 0862-9544 (Printed edition) Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovak Republic Telephone: + 421-2-60295111 Fax: + 421-2-65425882 e-Mail: amuc@fmph.uniba.sk Internet: www.iam.fmph.uniba.sk/amuc © 2013, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |