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Uniform estimates of positive solutions to quasi-linear differential equations

Authors:

I. V. Astashova

Abstract:

One considers the differential inequality

$y^n + sumlimits_{j = 0}^{n - 1} {a_j (x)y^{(j)} geqslant p * left| y right|^k } ,$

, where a _j(x) are continuous functions, p* > 0, n ≥ 1, k > 1, and its special case

$r_n (x)frac{d}{{dx}}left( {...frac{d}{{dx}}left( {r_1 (x)frac{d}{{dx}}(r_0 (x)y)} right)...} right) geqslant left| y right|^k ,$

, where all r _j(x) are sufficiently smooth positive functions. Uniform estimates are obtained for solutions defined in the same domain. __________ Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 26, pp. 27–36, 2007.

Keywords:

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