On the Positive Radial Solutions of a p-Laplacian Problem on an Unbounded Exterior Domain

The present paper establishes the existence of positive radial solutions to the p-Laplacien equation: \(\Delta _{p} u - u + u^{q}=0, \ p > 2\) and \(q>1,\) on an unbounded exterior domain \(\Omega _{e} \subset \mathbb {R}^{N},\) with zero initial datum. First, we provided a result on the existence of positive radial solutions using a shooting method and an associated energy function. Second we derived some important results on the asymptotic behavior of global solutions at infinity.