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POLYNOMIAL-PERIODIC SOLUTIONS OF DIFFERENTIAL-DIFFERENCE EQUATIONS

POLYNOMIAL-PERIODIC SOLUTIONS OF DIFFERENTIAL-DIFFERENCE EQUATIONS DEMONSTRATIO MATHEMATICAVol. ViliNo 11975Anna Wlodarska-DymitrukPOLYNOMIAL-PERIODIC SOLUTIONSOF DIFFERENTIAL-DIFFERENCE EQUATIONSConsider a system ofequations(1)non-lineardifferential-difference= 0(t,x(t),x(t-«,) t ... f x (t-u )) ,where x(t) = (x^(t),...,xn(t)) is an absolute continuous n-dimensional vector function and the given n-dimensional vectorfunction G(t ,u Q1 ,... ,u 0n ,... ,u ql ,... . u ^ ) of (q+l)n+1 variables is continuous. We say that vector function x(t) is a solution of system (1) if this system is satisfied by x(t) almost everywhere.We assume thatare real numbers and without loss ofgenerality that 0 = U q < c j 1 < c j 2 < . . .<We assume also that all numbers cj^ are commensurable,i.e. there is real number rj¿0 and there are positive integersn^ such that= n^r for i = 1,...,q. We put n Q = 0.Let u = Nr, where N is a common multipleofintegersand let X be a space of all continuous cj-periodicvector functions. We consider the space X of all vector functions x(t) such thatmx(t)eXiffx(t) = Y i SjcftH»k=0where all z^CtJeX^ . In the paper [l] were studied ¡¿-periodicsolutions of non-linear differential-difference equations. Inthis note we are looking for solutions in the space X.- 49 -2A,Wlodarska-Dymitruk1. A n a l g e b http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

POLYNOMIAL-PERIODIC SOLUTIONS OF DIFFERENTIAL-DIFFERENCE EQUATIONS

Wlodarska-Dymitruk, Anna
Demonstratio Mathematica , Volume 8 (1): 18 – Jan 1, 1975
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Publisher
de Gruyter
Copyright
© by Anna Wlodarska-Dymitruk
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-1975-0106
Publisher site
See Article on Publisher Site

Abstract

DEMONSTRATIO MATHEMATICAVol. ViliNo 11975Anna Wlodarska-DymitrukPOLYNOMIAL-PERIODIC SOLUTIONSOF DIFFERENTIAL-DIFFERENCE EQUATIONSConsider a system ofequations(1)non-lineardifferential-difference= 0(t,x(t),x(t-«,) t ... f x (t-u )) ,where x(t) = (x^(t),...,xn(t)) is an absolute continuous n-dimensional vector function and the given n-dimensional vectorfunction G(t ,u Q1 ,... ,u 0n ,... ,u ql ,... . u ^ ) of (q+l)n+1 variables is continuous. We say that vector function x(t) is a solution of system (1) if this system is satisfied by x(t) almost everywhere.We assume thatare real numbers and without loss ofgenerality that 0 = U q < c j 1 < c j 2 < . . .<We assume also that all numbers cj^ are commensurable,i.e. there is real number rj¿0 and there are positive integersn^ such that= n^r for i = 1,...,q. We put n Q = 0.Let u = Nr, where N is a common multipleofintegersand let X be a space of all continuous cj-periodicvector functions. We consider the space X of all vector functions x(t) such thatmx(t)eXiffx(t) = Y i SjcftH»k=0where all z^CtJeX^ . In the paper [l] were studied ¡¿-periodicsolutions of non-linear differential-difference equations. Inthis note we are looking for solutions in the space X.- 49 -2A,Wlodarska-Dymitruk1. A n a l g e b

Journal

Demonstratio Mathematica – de Gruyter

Published: Jan 1, 1975

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