Geodesic
Nonlinear homogeneous eigenvalue problem in $R^N$: nonstandard variational approach
Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) no. 3, pp. 421-431 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The nonlinear eigenvalue problem for p-Laplacian $$ \cases - \operatorname{div} (a(x) |\nabla u|^{p-2} \nabla u) = \lambda g (x) |u|^{p-2} u \text{ in } \Bbb R^N, \ u >0 \text{ in } \Bbb R^N, \mathop{\lim}\limits_{|x|\to \infty} u(x) = 0, \endcases $$ is considered. We assume that $1 p N$ and that $g$ is indefinite weight function. The existence and $C^{1, \alpha}$-regularity of the weak solution is proved.
The nonlinear eigenvalue problem for p-Laplacian $$ \cases - \operatorname{div} (a(x) |\nabla u|^{p-2} \nabla u) = \lambda g (x) |u|^{p-2} u \text{ in } \Bbb R^N, \ u >0 \text{ in } \Bbb R^N, \mathop{\lim}\limits_{|x|\to \infty} u(x) = 0, \endcases $$ is considered. We assume that $1 p N$ and that $g$ is indefinite weight function. The existence and $C^{1, \alpha}$-regularity of the weak solution is proved.
Classification : 35J65, 35J70, 35P30, 49J40, 49R50
Keywords: eigenvalue; the p-Laplacian; indefinite weight; regularity 
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     author = {Dr\'abek, Pavel and Moudan, Zakaria and Touzani, Abdelfettah},
     title = {Nonlinear homogeneous eigenvalue problem in $R^N$: nonstandard variational approach},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {421--431},
     year = {1997},
     volume = {38},
     number = {3},
     mrnumber = {1485065},
     zbl = {0940.35150},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1997_38_3_a0/}
}
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Drábek, Pavel; Moudan, Zakaria; Touzani, Abdelfettah. Nonlinear homogeneous eigenvalue problem in $R^N$: nonstandard variational approach. Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) no. 3, pp. 421-431. http://geodesic.mathdoc.fr/item/CMUC_1997_38_3_a0/