An eigenvalue problem involving a degenerate and singular elliptic operator

We study an eigenvalue problem involving a degenerate and singular elliptic operator on the whole space [R.sup.N]. We prove the existence of an unbounded and increasing sequence of eigenvalues. Our study generalizes to the case of degenerate and singular operators a result of A. Szulkin and M. Wille...

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Bibliographic Details
Published inBulletin of the Belgian Mathematical Society, Simon Stevin Vol. 18; no. 5; pp. 839 - 847
Main Authors Mihailescu, Mihai, Repovs, Dusan
Format Journal Article
LanguageEnglish
Published Belgian Mathematical Society 01.01.2011
The Belgian Mathematical Society
Subjects
35J20
35J60
35J70
Caffarelli-Kohn-Nirenberg inequality
degenerate and singular elliptic operator
Eigenvalue problem
Eigenvalues
Existence theorems
Operator theory
Sequences (Mathematics)
Hungary
Romania
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Summary:We study an eigenvalue problem involving a degenerate and singular elliptic operator on the whole space [R.sup.N]. We prove the existence of an unbounded and increasing sequence of eigenvalues. Our study generalizes to the case of degenerate and singular operators a result of A. Szulkin and M. Willem. 2000 Mathematics Subject Classification : 35J60, 35J20, 35J70. Key words and phrases : Eigenvalue problem, degenerate and singular elliptic operator, Caffarelli-Kohn-Nirenberg inequality.
ISSN:1370-1444
2034-1970
DOI:10.36045/bbms/1323787171