Solution of Ordinary Differential Equations by Series of Delta Functions

Abstract

Divergent series of Dirac delta functions have been used in the solution of ordinary and functional differential equations. Such divergent series also form the basic block in the asymptotic expansion of generalized functions. In this article we combine these two ideas and show that the series of deltas arising as solutions of ordinary differential equations can be realized as the asymptotics of distributional solutions of certain associated equations. © 1995 Academic Press, Inc.