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The following differential equation is considered in this paper:      $$y^{(n)} + p(x)\left| y \right|^{k - 1} y = 0, k > 1, p(x) \geqslant p_* > 0$$      . For positive solutions of this equation defined on the closed interval [a, b], the author obtains an upper estimate using a power function of (x − a) with coefficient depending only on n, k, and p.

On uniform estimates for positive solutions of nonlinear differential equations