Asymptotic Behavior of Solutions for Some Nonlinear Partial Differential Equations on Unbounded Domains

Abstract

We study the asymptotic behavior of positive solutions u of -∆pu(x) = V(x)u(x) p-1, p > 1; x ∈ Ω, and related partial differential inequalities, as well as conditions for existence of such solutions. Here, Ω contains the exterior of a ball in ℝN 1 < p < N, ∆p is the p-Laplacian and V is a nonnegative function. Our methods include generalized Riccati transformations, comparison theorems, and the uncertainty principle.