The Australian Journal of Mathematical Analysis and Applications


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Paper's Title:

On the Asymptotic Behavior of Solutions of Third Order Nonlinear Differential Equations

Author(s):

Ivan Mojsej and Alena Tartaľová

Institute of Mathematics,
Faculty of Science, P. J. Šafárik University,
Jesenná 5, 041 54 Košice,
Slovak Republic
ivan.mojsej@upjs.sk

Department of Applied Mathematics and Business Informatics,
Faculty of Economics, Technical University,
Nemcovej 32, 040 01 Košice,
Slovak Republic
alena.tartalova@tuke.sk


Abstract:

This paper is concerned with the asymptotic behavior of solutions of nonlinear differential equations of the third order with quasiderivatives. Mainly, we present the necessary and sufficient conditions for the existence of nonoscillatory solutions with specified asymptotic behavior as t tends to infinity. These conditions are presented as integral criteria and involve only the coefficients of investigated differential equations. In order to prove some of the results, we use a topological approach based on the Schauder fixed point theorem.


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