## Taiwanese Journal of Mathematics

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

#### 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

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

#### 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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