Nonexistence of positive solutions for a class of -Laplacian boundary value problems

We prove the nonexistence of positive radial solutions for the problem { − Δ p u = λ f ( u ) in  Ω , u = 0 on  ∂ Ω , where Δ p denotes the p -Laplacian, p > 1 , Ω is a ball or an annulus in R N , N > 1 , f : [ 0 , ∞ ) → R is at least p -linear,  f ( 0 ) < 0 , and is not required to be increasing or to have exactly one zero. Our results extend previous nonexistence results in the literature.