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) + åi=0n-1 ai(x)y(i) + p(x)|y|k-1y = 0

of even order n with k > 1 and continuous functions p(x) > 0 and ai(x). In the case where a0(x) º ... º an-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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