Geodesic
Eigenvalue problems with indefinite weight
Studia Mathematica, Tome 135 (1999) no. 2, pp. 191-201

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We consider the linear eigenvalue problem -Δu = λV(x)u, $u ∈ D^{1,2}_0(Ω)$, and its nonlinear generalization $-Δ_{p}u = λV(x)|u|^{p-2}u$, $u ∈ D^{1,p}_0(Ω)$. The set Ω need not be bounded, in particular, $Ω = ℝ^N$ is admitted. The weight function V may change sign and may have singular points. We show that there exists a sequence of eigenvalues $λ_n → ∞$.
DOI : 10.4064/sm-135-2-191-201
Keywords: eigenvalue problem, Laplacian, p-Laplacian, indefinite weight

Andrzej Szulkin 1 ;  1

1 
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Andrzej Szulkin;  . Eigenvalue problems with indefinite weight. Studia Mathematica, Tome 135 (1999) no. 2, pp. 191-201. doi: 10.4064/sm-135-2-191-201

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