In this paper we study the eigenvalue problem
where , is a bounded domain containing 0 in , is the p-Laplacean, and is a function related to Hardy-Sobolev inequality. The weight function may change sign and has nontrivial positive part. We study the simplicity, isolatedness of the first eigenvalue, nodal domain properties. Furthermore we show the existence of a nontrivial curve in the Fucik spectrum.
Submitted October 23, 2001. Published April 2, 2002.
Math Subject Classifications: 35J20, 35J70, 35P05, 35P30.
Key Words: p-Laplcean, Hardy-Sobolev operator, Fucik spectrum, Indefinite weight.
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|Konijeti Sreenadh |
Department of Mathematics
Indian Institute of Technology
Kanpur 208016, India.
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