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Regularity of the inversion problem for the Sturm-Liouville difference equation III. A criterion for regularity of the inversion problem.
- Source :
- Journal of Difference Equations & Applications; Mar2005, Vol. 11 Issue 3, p245-260, 16p
- Publication Year :
- 2005
-
Abstract
- We consider a difference equation where h?(0,h0],h0 is a fixed positive number, We obtain necessary and sufficient conditions under which assertions (I) and (II) hold together: (I) for a given p?[1,8), for any f?Lp(h),equation (1) has a unique solution y={yn(h)}n?Z?Lp(h) (regardless of h), and n?Z. (II) ?y?Lp(h)=c(p)??f??Lp(h) for any f?Lp(h). Here c(p) is an absolute positive constant, {Gn,m(h)}n,m?Z is the difference Green function corresponding to equation (1). [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10236198
- Volume :
- 11
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Journal of Difference Equations & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 16969716
- Full Text :
- https://doi.org/10.1080/10236190500044312