Nonexistence of nonnegative solutions for a class of (p−1)(p−1)-superhomogeneous semipositone problems

We establish nonexistence of nonnegative solutions to the BVP:−Δpu=λf(u)in B,u=0on ∂B, where λ>0λ>0 is a spectral parameter, Δp=defdiv(|∇u|p−2∇u) is the p  -Laplacian operator for p>1p>1 and B   is a unit ball in RNRN, N⩾2N⩾2. Here f   is a C1C1 nondecreasing function which satisfies f(0)<0f(0)<0 and additional asymptotic condition at ∞.