The WKB method and dichotomy for ordinary differential equations (Q2455281)

The author gives effective estimates for \(\varepsilon_{1,2}(x)\) in the fundamental system of solutions \[ y_{1,2}(x) = Q^{-1/4}(x)\exp \biggl(\mp\int_{x_0}^x\sqrt{Q(t)}\,dt\biggr) (1 + \varepsilon_{1,2}(x)) \] for the ordinary differential equation \[ -y'' + Q(x)y = 0, \tag{1} \] where \(Q\) is continuous and satisfies \(Q(x) > 0.\) For a fairly large class of functions \(Q,\) equation (1) is dichotomous. Estimates for the growth (decrease) rate of solutions are obtained.