Eigenvalue problems with indefinite weight
Andrzej Szulkin, Michel Willem · 1999
We consider the linear eigenvalue problem −∆u = λV (x)u, u ∈ D1,2 0 (Ω), and its nonlinear generalization −∆pu = λV (x)|u|p−2u, u ∈ D1,p0 (Ω). The set Ω need not be bounded, in par-ticular, Ω = RN is admitted. The weight function V may change sign and may have singular points. We show that there exists a sequence of eigenvalues λn →∞. 1