## Taiwanese Journal of Mathematics

### ASYMPTOTIC ANALYSIS OF FOURTH ORDER QUASILINEAR DIFFERENTIAL EQUATIONS IN THE FRAMEWORK OF REGULAR VARIATION

#### Abstract

Under the assumptions that $p(t),\;q(t)$ are regularly varying functions satisfying condition $$\int_a^\infty\frac{dt}{p(t)^{\frac{1}{\alpha}}}=\infty,$$ existence and asymptotic form of regularly varying intermediate solutions  are studied for a fourth-order quasilinear differential equation $$\left(p(t)|x''(t)|^{\alpha-1}\,x''(t)\right)^{\prime\prime}+q(t)|x(t)|^{\beta-1}\,x(t)=0,\quad \alpha \gt \beta\gt 0.$$ It is shown that the asymptotic behavior of all such solutions is governed by a unique explicit law.

#### Article information

Source
Taiwanese J. Math., Volume 19, Number 5 (2015), 1415-1456.

Dates
First available in Project Euclid: 4 July 2017

https://projecteuclid.org/euclid.twjm/1499133717

Digital Object Identifier
doi:10.11650/tjm.19.2015.5048

Mathematical Reviews number (MathSciNet)
MR3412014

Zentralblatt MATH identifier
1357.34070

#### Citation

Milošević, Jelena; Manojlović, Jelena V. ASYMPTOTIC ANALYSIS OF FOURTH ORDER QUASILINEAR DIFFERENTIAL EQUATIONS IN THE FRAMEWORK OF REGULAR VARIATION. Taiwanese J. Math. 19 (2015), no. 5, 1415--1456. doi:10.11650/tjm.19.2015.5048. https://projecteuclid.org/euclid.twjm/1499133717

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