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Advanced topics in difference equations
- Publisher
- Springer Journals
- Copyright
- Copyright © 1999 by Plenum Publishing Corporation
- Subject
- Mathematics; Mathematics, general
- ISSN
- 1072-947X
- eISSN
- 1572-9176
- DOI
- 10.1023/A:1022914213997
- Publisher site
- See Article on Publisher Site
Abstract
We consider the boundary value problem $$y^{(n)} (t) = P(t,y),{\text{ }}t \in (0,1)$$ $$y^{(i)} (ti) = 0,{\text{ }}j = 0,...,n_i - 1,{\text{ }}i = 1,...,r,$$ where r ≥ 2, n i ≥ 1 for i = 1, ... ,r, $$\sum {_{i = 1}^r = n}$$ and 0 = t 1 < t 2 < ... < t r = 1. Criteria are offered for the existence of double and triple ‘positive’ (in some sense) solutions of the boundary value problem. Further investigation on the upper and lower bounds for the norms of these solutions is carried out for special cases. We also include several examples to illustrate the importance of the results obtained.
Journal
Georgian Mathematical Journal – Springer Journals
Published: Oct 20, 2004