Geodesic
Eigenvalues of the $p$-Laplacian in ${\boldkey R}^N$ with indefinite weight
Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) no. 3, pp. 519-527.

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We consider the nonlinear eigenvalue problem $$ -\operatorname{div}(|{\nabla} u|^{p-2}{\nabla} u)=\lambda g(x)|u|^{p-2}u $$ in $\boldkey R^N$ with $p>1$. A condition on indefinite weight function $g$ is given so that the problem has a sequence of eigenvalues tending to infinity with decaying eigenfunctions in ${W^{1, p}(\boldkey R^N)}$. A nonexistence result is also given for the case $p\geq N$.
Classification : 35J65, 35J70, 35P30, 58E05
Keywords: eigenvalue; the $p$-Laplacian; indefinite weight; $\boldkey R^N$ 
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     author = {Huang, Yin Xi},
     title = {Eigenvalues of the $p${-Laplacian} in ${\boldkey R}^N$ with indefinite weight},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {519--527},
     publisher = {mathdoc},
     volume = {36},
     number = {3},
     year = {1995},
     mrnumber = {1364493},
     zbl = {0839.35097},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1995__36_3_a13/}
}
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Huang, Yin Xi. Eigenvalues of the $p$-Laplacian in ${\boldkey R}^N$ with indefinite weight. Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) no. 3, pp. 519-527. http://geodesic.mathdoc.fr/item/CMUC_1995__36_3_a13/