Generalized Inverses of Linear Differential Operators.

摘要

In recent years there has been much activity in the area of generalized inverses of linear operators. It is the purpose of this paper to discuss generalized inverses of linear operators generated by ordinary linear differential equations with a view to examination of an entire class of such inverses. The class of inverses considered includes as special cases the analogue of the Moore-Penrose generalized inverse for matrices and the group inverse for square matrices. The author also discusses the application of such inverses in problems of branching of solutions of nonlinear boundary-value problems. (Author)