FPM 2006, vol. 12, no. 5, pp. 3-9

FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2006, VOLUME 12, NUMBER 5, PAGES 3-9

On uniform estimates for solutions to quasi-linear differential equations

I. V. Astashova

Abstract

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Uniform estimates are obtained for positive solutions with the same domain to the equation

y

⁽ⁿ⁾ + å_i=0^n-1 a_i(x)y⁽ⁱ⁾ + p(x)|y|^k-1y = 0

of even order $n$ with $k > 1$ and continuous functions $p(x) >
0$ and $a$ _i(x). In the case where $a$ ₀(x) º ... º a_n-1(x) º 0, uniform estimates are obtained depending on $p$ _* = inf p(x) > 0 and not on the function $p(x)$ itself.

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