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The existence of positive radial solutions of the equation -din( |Du|p-2Du)=f(u) is studied in annular domains in Rn,n≥2. It is proved that if f(0)≥0, f is somewherenegative in (0,∞), limu→0^+f' (u)=0 and limu→∞ (f(u)/u^p-1)=∞, then there is alarge po