Discussion on ''The boundedness and asymptotic behavior of solutions of differential system of second order with variable coefficients'' (Q1058647)

This paper considers the paper by \textit{L. Li} (*) in ibid. 3, 541-547 (1982; Zbl 0512.34029). The author points out that there are some errors in (*), for example: \(\beta\) should be a complex value function in an interval \([t_ 0,\infty)\), \(\Delta\) should be \(\Delta =ad-bc\neq 0\), equation \(d^ 2Z_ i/dt^ 2+p_ iZ_ i=0\) and not \(dZ_ i/dt+p_ iZ_ i=0\), all definition intervals should be \([t_ 0,\infty)\) and not \((t_ 0,\infty)\), in theorems 1,2 the conclusion must be \(\int^{t}_{0}| p_ i| dt\leq 4/T\) and not \(\int^{t}_{0}| p_ i| dt\leq T/4\) \((i=1,2)\) etc. To the conditions of theorems 1-5 should be added the condition ''There is no zero point for \(t\in [t^*,\infty)\) as \(t^*>t_ 0''\). The conclusion of theorems 1,2 is the same in essence as that of Yurovskij and Starzhinskij and the theorems 3,4 lack an important condition, i.e. \(p_ i(t)\) \((i=1,2)\) is a bounded variation function as \(t\in [t_ 0,\infty)\). It seems that it is not easy to accomplish this.