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

View as HTML
View as gif image

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-1}y = 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.

Location: http://mech.math.msu.su/~fpm/eng/k06/k065/k06501h.htm

Last modified: February 21, 2007