6533b825fe1ef96bd128206c
RESEARCH PRODUCT
Integration of a Dirac comb and the Bernoulli polynomials
Maria Alice BertolimAlain JacquemardGioia M. Vagosubject
Bernoulli differential equationDifferential equations[ MATH ] Mathematics [math]Differential equationGeneral MathematicsBernoulli polynomials010102 general mathematicsMathematical analysisDirac combPiecewise-smooth01 natural sciencesDirac comb010305 fluids & plasmasBernoulli polynomialsPeriodic functionsymbols.namesakeDistribution (mathematics)Ordinary differential equation0103 physical sciencessymbols[MATH]Mathematics [math]0101 mathematicsBernoulli processMathematicsMSC: 34A36 37B55 11B68 70G60description
Abstract For any positive integer n , we consider the ordinary differential equations of the form y ( n ) = 1 − Ш + F where Ш denotes the Dirac comb distribution and F is a piecewise- C ∞ periodic function with null average integral. We prove the existence and uniqueness of periodic solutions of maximal regularity. Above all, these solutions are given by means of finite explicit formulae involving a minimal number of Bernoulli polynomials. We generalize this approach to a larger class of differential equations for which the computation of periodic solutions is also sharp, finite and effective.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2016-03-01 |