To the question of stability with respect to nonlinear approximation
The system of ordinary differential equations \[ \dot{x}_s = f_s (x) + \sum_{j=1}^{k} b_{sj} (t) h_j (x), \qquad s = 1,\ldots,n, \tag{1} \] is considered. Here, \(f_s(x)\) and \(h_j(x)\) are continuously differentiable homogeneous functions of order \(\mu\) and \(\sigma\) respectively; \(\mu >1\) and \(\sigma >1\) are rational numbers with odd denominators. The functions \(b_{sj} (t)\) are continuous and bounded for all \(t \geq 0\). The author obtains conditions under which the asymptotic stability of the trivial solution to (1) follows from the asymptotic stability of the trivial solution to the nonperturbed system \[ \dot{x}_s = f_s (x), \qquad s = 1,\ldots,n . \]
scientific article; zbMATH DE number 1431680