Open Access
Translator Disclaimer
2013 EXISTENCE AND ASYMPTOTIC BEHAVIOR OF POSITIVE SOLUTIONS OF FOURTH ORDER QUASILINEAR DIFFERENTIAL EQUATIONS
Kusano Takaŝi, Jelena Manojlović, Tomoyuki Tanigawa
Taiwanese J. Math. 17(3): 999-1030 (2013). DOI: 10.11650/tjm.17.2013.2496

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.

Citation

Download Citation

Kusano Takaŝi. Jelena Manojlović. Tomoyuki Tanigawa. "EXISTENCE AND ASYMPTOTIC BEHAVIOR OF POSITIVE SOLUTIONS OF FOURTH ORDER QUASILINEAR DIFFERENTIAL EQUATIONS." Taiwanese J. Math. 17 (3) 999 - 1030, 2013. https://doi.org/10.11650/tjm.17.2013.2496

Information

Published: 2013
First available in Project Euclid: 10 July 2017

zbMATH: 1293.34063
MathSciNet: MR3072274
Digital Object Identifier: 10.11650/tjm.17.2013.2496

Subjects:
Primary: 26A12 , 34C11

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

Rights: Copyright © 2013 The Mathematical Society of the Republic of China

JOURNAL ARTICLE
32 PAGES


SHARE
Vol.17 • No. 3 • 2013
Back to Top