Radial entire solutions of the linear equation $\Delta u+łambda p(\vert x\vert )u=0$
Manabu Naito · Hiroshima Mathematical Journal · 1989
We are concerned with radial entire solutions of the linear elliptic differential equation Δu+λp(|x|)u=0, x∈R N , where Δ is the N-dimensional Laplacian, |x| denotes the Euclidean length of x∈R N , and λ is a positive parameter. We always assume that N≥3 and p satisfies p∈C[0, ∞), p(t)≥0 on [0, ∞), and p(t)÷ on [T, ∞) for every T≥0