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On measure of noncompactness in lebesgue and sobolev spaces with an application to the functional integro-differential equation.
- Source :
-
Aequationes Mathematicae . Feb2023, Vol. 97 Issue 1, p199-217. 19p. - Publication Year :
- 2023
-
Abstract
- In this paper we attempt to define axiomatic measures of non-compactness for Sobolev spaces of integer order W n , p (Ω) , where Ω ⊂ R d (which is equivalent to Ω being any set of infinite measure). We consider two cases, one with Ω being an open subset with finite measure, and another when Ω = R d , and discuss basic features of the measure of non-compactness in each case. Next we define a partial measure of non-compactness on space L p (Ω ; B) , where B is a Banach space. Furthermore, we give some application to solve the functional integro-differential equation in W 1 , p (Ω). [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00019054
- Volume :
- 97
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Aequationes Mathematicae
- Publication Type :
- Academic Journal
- Accession number :
- 161607838
- Full Text :
- https://doi.org/10.1007/s00010-022-00906-1