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Some Topological Properties of Solution Sets in a Second Order Differential Inclusion with m-point Boundary Conditions.
- Source :
- Set-Valued & Variational Analysis; Jun2012, Vol. 20 Issue 2, p249-277, 29p
- Publication Year :
- 2012
-
Abstract
- We consider a class of m-point ( m > 3) second order boundary value problem ( $\cal{P}_{F}$) in a separable Banach space E of the form [MediaObject not available: see fulltext.]where F is a closed valued mapping. Under suitable compactness conditions on F we prove that the $W ^{2, 1}_E([0, 1])$-solutions of ( $\cal{P}_{F}$) is compact and is a retract in $C^1_E([0, 1])$. A new existence result of $W ^{2, 1}_E([0, 1])$-solutions and a related relaxation problem are also provided, here F is no longer bounded. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 18770533
- Volume :
- 20
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- Set-Valued & Variational Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 74551063
- Full Text :
- https://doi.org/10.1007/s11228-011-0200-1