Eigenvalues of the $p$-Laplacian in ${\boldkey R}^N$ with indefinite weight
Huang, Yin Xi
Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995), p. 519-527 / Harvested from Czech Digital Mathematics Library
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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 $p\geq N$.

Publié le : 1995-01-01
Classification:  35J65,  35J70,  35P30,  58E05 
@article{118781,
     author = {Yin Xi Huang},
     title = {Eigenvalues of the $p$-Laplacian in ${\boldkey R}^N$ with indefinite weight},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {36},
     year = {1995},
     pages = {519-527},
     zbl = {0839.35097},
     mrnumber = {1364493},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118781}
}

Huang, Yin Xi. Eigenvalues of the $p$-Laplacian in ${\boldkey R}^N$ with indefinite weight. Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) pp. 519-527. http://gdmltest.u-ga.fr/item/118781/

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