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Existence and Precise Asymptotics of Positive Solutions for a Class of Nonlinear Differential Equations of the Third Order by Jaroslav Jaroš; Takaŝi Kusano; Tomoyuki Tanigawa is a Mathematics article available to read on EtoBox.

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Our purpose here is to show that an application of the theory of regular variation (in the sense of Karamata) gives the possibility of determining the existence and precise asymptotic behavior of positive solutions of the third-order nonlinear differential equation ....x 0 / ̨1 / 0 / ̨2 / 0 C q.t /x ˇ D 0, where ̨1; ̨2 and ˇare positive constants satisfying ̨1 ̨2 > ˇ, q W OEa; 1/ ! .0; 1/ is a continuous regularly varying function and u D juj sgn u, > 0; u 2 R.

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Author

Jaroslav Jaroš; Takaŝi Kusano; Tomoyuki Tanigawa

Publisher

Walter de Gruyter GmbH

Published

2013

Language

EN

Field

Mathematics (Physical Sciences)