A Green's Function Convergence Principle, with Applications to Computation and Norm Estimates.

摘要

A new tool is developed for the study of Green's functions of multipoint boundary value problems for kth order linear ordinary scalar equations. The tool makes the form of a convergence principle for Green's functions, and is the proper version of a continuity theorem for boundary value problems. Two types of applications are considered: practical computation of Green's functions and norm estimates for Green's functions in the spaces Cn(a,b) and L(1)(a,b). Special attention is given to frequently used equations and boundary conditions, in particular, the equation y to the kth power = 0 is studied in detail for 2-point and multipoint boundary conditions. (Author)