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

Takaŝi Kusano, Jelena Manojlović, Tomoyuki Tanigawa

Type: Article

Publication Date: 2013-05-01

Citations: 3

DOI: https://doi.org/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.

Locations

Taiwanese Journal of Mathematics - View - PDF

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