Nonexistence of Positive Solutions of PDE's with p-Laplacian

Abstract

We derive conditions on the function c : Rⁿ → R which guarantee that the PDE with p-Laplacian div (❘∇ u❘^p-2∇ u ) + c(x)❘u❘^p-2u =0, p >1, has no positive solution either in Rⁿ or in the domain Omega_r :={x ∈ Rⁿ : ❘x❘ ≧r} with r arbitrarily large.