PORTUGALIAEMATHEMATICA
Vol. 57, No. 1, pp. 17-33 (2000)
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PORTUGALIAE MATHEMATICA Vol. 57, No. 1, pp. 17-33 (2000) |
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Asymptotic Behavior of Solutions of Second Order Nonlinear Differential EquationsSvitlana P. Rogovchenko and Yuri V. RogovchenkoDepartment of Mathematics, Eastern Mediterranean University,Famagusta, TRNC, Mersin 10 - TURKEY E-mail: svitlana.as@mozart.emu.edu.tr Department of Mathematics, Eastern Mediterranean University, Famagusta, TRNC, Mersin 10 - TURKEY and Institute of Mathematics, National Academy of Sciences, 252601 Kyiv, UKRAINE E-mail: yuri@mozart.emu.edu.tr, yuri@imat.gluk.apc.org Abstract: We study asymptotic properties of solutions for certain classes of second order nonlinear differential equations. The main purpose is to investigate when all continuable solutions or just a part of them with initial data satisfying an additional condition behave at infinity like nontrivial linear functions. Making use of Bihari's inequality and its derivatives due to Dannan, we obtain results which extend and complement those known in the literature. Examples illustrating the relevance of the theorems are discussed. Keywords: Second order; nonlinear differential equation; continuable solutions; asymptotic behavior; Bihari's inequality. Classification (MSC2000): 34D05.; 34A34, 34C05. Full text of the article:
Electronic version published on: 31 Jan 2003. This page was last modified: 27 Nov 2007.
© 2000 Sociedade Portuguesa de Matemática
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