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

We establish nonexistence of nonnegative solutions to the BVP: −Δpu = λf (u) in B, u =0 on∂B, where λ > 0 is a spectral parameter, Δp def = div(|∇u|p−2∇u) is the p-Laplacian operator for p >1 and B is a unit ball in RN, N 2. Here f is a C1 nondecreasing function which satisfies f (0) < 0 and additional asymptotic condition at∞. © 2005 Elsevier Inc. All rights reserved