On the asymptotic behavior of solutions to nonlinear ordinary differential equations

Article type: Research Article

Authors: Agarwal, Ravi P. | Djebali, Smail | Moussaoui, Toufik | Mustafa, Octavian G. | Rogovchenko, Yuri V.

Affiliations: Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901, USA. E-mail: [email protected] | Department of Mathematics, E.N.S., P.O. Box 92, 16050 Kouba, Algiers, Algeria. E-mails: {djebali,moussaoui}@ens-kouba.dz | Department of Mathematics, University of Craiova, Al. I. Cuza 13, Craiova, Romania. E-mail: [email protected] | Department of Mathematics, Eastern Mediterranean University, Famagusta, TRNC, Mersin 10, Turkey. E-mail: [email protected]

Abstract: We discuss a number of issues important for the asymptotic integration of ordinary differential equations. After developing the tools required for application of the fixed point theory in the investigation, we present some general results about the long-time behavior of solutions of n-th order nonlinear differential equations with an emphasis on the existence of polynomial-like solutions, the asymptotic representation for the derivatives and the effect of perturbations upon the asymptotic behavior of solutions.

Journal: Asymptotic Analysis, vol. 54, no. 1-2, pp. 1-50, 2007