Second order elliptic equations with degenerate weight

Author:
W. Allegretto

Journal:
Proc. Amer. Math. Soc. **107** (1989), 989-998

MSC:
Primary 35J10; Secondary 35P15, 47F05

DOI:
https://doi.org/10.1090/S0002-9939-1989-0977929-4

MathSciNet review:
977929

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Abstract: We consider the eigenvalue problem: , in a smooth bounded domain . We allow to have negative spectrum and assume in in a subdomain of . Under suitable regularity conditions, we establish several results for the spectrum of this problem. In particular, we give: a min.max. formula for ; a precise estimate on the number of negative ; an estimate for the location of negative . An example concludes the paper.

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DOI:
https://doi.org/10.1090/S0002-9939-1989-0977929-4

Article copyright:
© Copyright 1989
American Mathematical Society