Open AccessOrdinary differential equations with delta function terms
Author(s) -
Marko Nedeljkov,
Michael Oberguggenberger
Publication year - 2012
Publication title -
publications de l'institut mathématique
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.246
H-Index - 17
eISSN - 1820-7405
pISSN - 0350-1302
DOI - 10.2298/pim1205125n
Subject(s) - dirac delta function , nonlinear system , multiplicative function , mathematics , ordinary differential equation , function (biology) , limiting , delta , mathematical analysis , order (exchange) , differential equation , pure mathematics , physics , mechanical engineering , finance , quantum mechanics , astronomy , evolutionary biology , engineering , economics , biology
summary:Models of singularities given by discontinuous functions or distributions by means of generalized functions of Colombeau have proved useful in many problems posed by physical phenomena. In this paper, we introduce in a systematic way generalized functions that model singularities given by distributions with singular point support. Furthermore, we evaluate various products of such generalized models when the results admit associated distributions. The obtained results follow the idea of a well-known result of Jan Mikusiński on balancing of singular distributional products