The aim of this paper is to prove the nonexistence of positive radial solutions to the problem -Δ_ϕu=λf (u), x B₁ (0), u (x) =0 on |x|=1, for λ>0 sufficiently large. Here, ϕ is a continuous function, Δ_ϕ denotes the ϕ-Laplacian operator which is defined by Δ_ϕ (u): =div (ϕ (| u|) u), and B₁ (0) is the unit ball in RN, with N>1. Furthermore, f is a continuous, nondecreasing function such that f (0) <0, and its behavior at infinity is intimately related to ϕ. Our findings are presented in a combined format, employing both an indirect argument and an energy analysis.
Herrón et al. (Fri,) studied this question.