Geodesic
On uniform estimates for solutions to quasi-linear differential equations
Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 5, pp. 3-9.

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Uniform estimates are obtained for positive solutions with the same domain to the equation $$ y^{(n)}+\sum_{i=0}^{n-1}a_{i}(x)y^{(i)}+p(x)|y|^{k-1}y=0 $$ of even order $n$ with $k>1$ and continuous functions $p(x)>0$ and $a_i(x)$. In the case where $a_{0}(x)\equiv\dots\equiv a_{n-1}(x)\equiv0$, uniform estimates are obtained depending on $p_{*}=\inf p(x)>0$ and not on the function $p(x)$ itself. 
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I. V. Astashova. On uniform estimates for solutions to quasi-linear differential equations. Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 5, pp. 3-9. http://geodesic.mathdoc.fr/item/FPM_2006_12_5_a0/

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[2] Kondratev V. A., “O kachestvennykh svoistvakh reshenii polulineinykh ellipticheskikh uravnenii”, Tr. seminara im. I. G. Petrovskogo, no. 16, 1991, 186–190

[3] Astashova I. V., “Estimates of solutions to one-dimensional Schredinger equation”, Progress in Analysis. Proc. of the 3rd Int. ISAAC Congress, II, World Sci. Press, 2003, 955–960 | MR