Existence of an interval of principal eigenvalues for radially symmetric problems on all of RN

摘要

We investigate the existence of principal eigenvalues, i.e., values of λ for which the corresponding eigenfunction is positive, for the radially symmetric problem -Δu(x)=λg(x)u(x) for x∈RN, where g is a radially symmetric smooth bounded function which changes sign on [0,∞).