Taiwanese Journal of Mathematics

EXISTENCE AND ASYMPTOTIC BEHAVIOR OF POSITIVE SOLUTIONS OF FOURTH ORDER QUASILINEAR DIFFERENTIAL EQUATIONS

Kusano Takaŝi, Jelena Manojlović, and Tomoyuki Tanigawa

Full-text: Open access

Abstract

The feature of the present work is to demonstrate that the method of regular variation can be effectively applied to fourth order quasilinear differential equations of the forms \begin{equation*} (|x''|^{\alpha-1}x'')'' + q(t)|x|^{\beta-1}x = 0, \end{equation*} under the assumptions that $\alpha \gt \beta$ and $q(t): [a,\infty) \to (0,\infty)$ is regularly varying function, providing full information about the existence and the precise asymptotic behavior of all possible positive solutions.

Article information

Source
Taiwanese J. Math., Volume 17, Number 3 (2013), 999-1030.

Dates
First available in Project Euclid: 10 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499705996

Digital Object Identifier
doi:10.11650/tjm.17.2013.2496

Mathematical Reviews number (MathSciNet)
MR3072274

Zentralblatt MATH identifier
1293.34063

Subjects
Primary: 34C11: Growth, boundedness 26A12: Rate of growth of functions, orders of infinity, slowly varying functions [See also 26A48]

Keywords
fourth-order differential equations regularly varying solutions slowly varying solutions asymptotic behavior of solutions positive solutions

Citation

Takaŝi, Kusano; Manojlović, Jelena; Tanigawa, Tomoyuki. EXISTENCE AND ASYMPTOTIC BEHAVIOR OF POSITIVE SOLUTIONS OF FOURTH ORDER QUASILINEAR DIFFERENTIAL EQUATIONS. Taiwanese J. Math. 17 (2013), no. 3, 999--1030. doi:10.11650/tjm.17.2013.2496. https://projecteuclid.org/euclid.twjm/1499705996


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