Distributions, their primitives and integrals with applications to differential equations

2013/01/03 by Seppo Heikkilä, Heikkilä, Seppo, Erik Talvila +1
Mathematics · #26A15 #26A24 #26A39 #34A12 #34A34 #34A36 #39B12 #39B22 #46E30 #46F05 #46F10 #46G12 #47H07 #47H10 #47J25 #58D25 (Primary) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:26A15 #msc:26A24 #msc:26A39 #msc:34A12 #msc:34A34 #msc:34A36 #msc:39B12 #msc:39B22 #msc:46E30 #msc:46F05 #msc:46F10 #msc:46G12 #msc:47H07 #msc:47H10 #msc:47J25 #msc:58D25

paper · pdf · doi:10.48550/arxiv.1301.0505

arxiv created 2013/01/03 · arxiv updated 2013/01/04

Abstract

In this paper we will study integrability of distributions whose primitives are left regulated functions and locally or globally integrable in the Henstock--Kurzweil, Lebesgue or Riemann sense. Corresponding spaces of distributions and their primitives are defined and their properties are studied. Basic properties of primitive integrals are derived and applications to systems of first order nonlinear distributional differential equations and to an mth order distributional differential equation are presented. The domain of solutions can be unbounded, as shown by concrete examples.

Related

• The regulated primitive integral
• The continuous primitive integral in the plane
• Integrals and Banach spaces for finite order distributions
• The distributional Denjoy integral
• Integrability of weak distributions on Banach manifolds