Geodesic
On the eigenvalue problem for the Hardy-Sobolev operator with indefinite weights
Electronic journal of differential equations, Tome 2002 (2002)
In this paper we study the eigenvalue problem

$ -\Delta_{p}u-a(x)|u|^{p-2}u=\lambda |u|^{p-2}u, \quad u\in W^{1,p}_{0}(\Omega), $

where $1 less than p\le N, $Omega$ is a bounded domain containing 0 in $mathbbR^N, Delta_p$ is the p-Laplacean, and $a(x)$ is a function related to Hardy-Sobolev inequality. The weight function $V(x)inL^s(Omega)$ 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.$
Classification : 35J20, 35J70, 35P05, 35P30
Keywords: p-laplcean, Hardy-Sobolev operator, Fucik spectrum, indefinite weight 
@article{EJDE_2002__2002__a71,
     author = {Sreenadh,  K.},
     title = {On the eigenvalue problem for the {Hardy-Sobolev} operator with indefinite weights},
     journal = {Electronic journal of differential equations},
     year = {2002},
     volume = {2002},
     zbl = {1125.35332},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a71/}
}
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%A Sreenadh,  K.
%T On the eigenvalue problem for the Hardy-Sobolev operator with indefinite weights
%J Electronic journal of differential equations
%D 2002
%V 2002
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Sreenadh,  K. On the eigenvalue problem for the Hardy-Sobolev operator with indefinite weights. Electronic journal of differential equations, Tome 2002 (2002). http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a71/