Uniqueness to quasilinear problems for the p-Laplacian in radially symmetric domains

The perturbed boundary value problem, -Δpu = λup-1-uq+g(u) in Ω, u = 0 on ∂Ω was proved, where p>2, q>p-1 and Ω is a bounded radially symmetric domain D, D is either a ball B = (x∈RN:|x|<R) or an annulus A = (x∈RN:a<|x|<R), a, R positive, admits a unique positive solution when λ>0 is large, provided that the perturbation term g = g(u) is C1 and satisfies the growth conditions g = o(up-1) as u→0+, g = o(uq) as u→+∞. As explicit examples show in the case p = 2, uniqueness for large λ is the best possible result since multiple solutions could appear for particular g's when λ is of the order of λ1, p.