Multiplicity Results of Positive Radial Solutions for p-Laplacian Problems in Exterior Domains

Abstract

We find the second positive radial solution for the following p-Laplacian problem: div(|∇u|p−2∇u)+K(|x|)uq=0 in Ω, u|∂Ω=0, u(x)→μ>0 as |x|→∞, where Ω={x∈ℝN:|x|>r0}, r0>0, N>p>1, K∈C(Ω,(0,∞)) and q>p−1. We also give some global existence results with respect to the parameter μ.