METHODS FOR TRANSFORMATIONS OF GAUSS AND STURM - LIOUVILLE TYPE EQUATIONS

The methods for discrete-group classification of the ordinary differential equation classes are considered. The discrete-group analysis of the hypergeometric Gauss equation and classes of the ordinary differential equations connected with it, with application of the results of the theory of finite groups and theory of graphs has been made. The new integrated cases of the hypergeometric Gauss equations have been obtained. The new approach to the formulation and solution of the inverse discrete-group problems realized as an example of the class of Sturm - Liouville type equations has been proposed. The properties in solutions of some classes of the second order non-linear differential equations obtained at solution of the inverse discrete-group problem have been investigatedAvailable from VNTIC / VNTIC - Scientific & Technical Information Centre of RussiaSIGLERURussian Federatio