Sibuya Y. Global Theory of a Second Order Linear Ordinary Differential Equation With a Polynomial Coefficent

North Holland, 1975. - 290 Pages.The general theory of asymptotic solutions a t an irregular singular point i s one of many remarkable achievements of the research concerning linear ODEs i n the complex domain. However, in the case when differential equations contain auxiliary parameters, the general theory has not been completed with regard t o the behavior o f asymptotic solutions as functions of these parameters. As for the Stokes phenomena (i .e. the relations among asymptotic solutions), the research has been conducted so far only i n various particular cases. In applications, there are several well-established asymptotic methods based on integral representations of solutions. * In most cases, these methods are satisfactory. Nevertheless, the theory of differential equations at irregular singular points has been given a number of opportunities to show its strength in applications, even when integral representations of solutions are available.