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Keywords:
eigenvalue; the p-Laplacian; indefinite weight; regularity
eigenvalue; the p-Laplacian; indefinite weight; regularity
Summary:
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.
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