On the eigenvalues of the -Laplacian

with varying

Author:
Yin Xi Huang

Journal:
Proc. Amer. Math. Soc. **125** (1997), 3347-3354

MSC (1991):
Primary 35P30, 35B30

DOI:
https://doi.org/10.1090/S0002-9939-97-03961-0

MathSciNet review:
1403133

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Abstract | References | Similar Articles | Additional Information

Abstract: We study the nonlinear eigenvalue problem

where , is a bounded smooth domain in . We prove that the first and the second variational eigenvalues of (1) are continuous functions of . Moreover, we obtain the asymptotic behavior of the first eigenvalue as and .

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Additional Information

**Yin Xi Huang**

Affiliation:
Department of Mathematical Sciences, University of Memphis, Memphis, Tennessee 38152

Email:
huangy@mathsci.msci.memphis.edu

DOI:
https://doi.org/10.1090/S0002-9939-97-03961-0

Keywords:
Eigenvalues,
the $p$-Laplacian

Received by editor(s):
June 14, 1996

Additional Notes:
Research is partly supported by a University of Memphis Faculty Research Grant

Communicated by:
Palle E. T. Jorgensen

Article copyright:
© Copyright 1997
American Mathematical Society