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In the recent years, many results have been established on positive solutions for boundary value problems of the form $-div\left(\right|\nabla u\left(x\right){|}^{p-2}\nabla u\left(x\right))=\lambda f\left(u\left(x\right)\right)$ in Ω, u(x)=0 on ∂Ω, where λ > 0, Ω is a bounded smooth domain and f(s) ≥ 0 for s ≥ 0. In this paper, a priori estimates of positive radial solutions are presented when N > p > 1, Ω is an N-ball or an annulus and f ∈ C¹(0,∞) ∪ C⁰([0,∞)) with f(0) < 0 (non-positone).