On uniform estimates for solutions to quasi-linear differential equations

Abstract

We obtain uniform estimates for positive solutions with the same domain to the equation $$y^{(n)} + \sum\limits_{i = 0}^{n - 1} {a_i (x)y^{(i)} } + p(x)\left| y \right|^{k - 1} y = 0$$ of even order n with k > 1 and continuous functions p(x) > 0 and a i (x). In the case where a 0(x) ≡ ⋯ ≡ a n−1(x) ≡ 0, the uniform estimates obtained depend on p = inf p(x) > 0 and are independent of the function p(x) itself.