We investigate the existence of positive principal eigenvalues of the problem − Δu(x) = λg(x)u for x ϵ Rn; u(x) → 0 as x → ∞ where the weight function g changes sign on Rn. It is proved that such eigenvalues exist if g is negative and bounded away from 0 at ∞ or if n ≥ 3 and |g(x)| is sufficiently small at ∞ but do not exist if n = 1 or 2.
- Elliptic boundary value problems
- Indefinite weight function
- Spectral theory
ASJC Scopus subject areas
- Applied Mathematics