Asymptotics at infinity of solutions for p-Laplace equations in exterior domains

Abstract

Let 1 < p < N, and u be a nonnegative solution of -Delta(p)u = f (x, u) on R-N\(B-1) over bar where f behaves like \x\(-l)u(q) near \x\ = infinity and u = 0, for some constants q >= 0 and l is an element of R. We obtain asymptotic decay estimates for u. In particular, our results complete the 'sublinear case' q < p - 1. A related analysis is carried out for systems like -Delta(p)u = f(x, v), -Delta(p)v = g(x, u), where p = 2 corresponds to a Hamiltonian system. In this way we extend and improve some known results of Mitidieri and Pohozaev, Bidaut-Veron and Pohozaev, and other authors. Our proofs use tools such as Harnack inequality, the Maximum Principle, Liouville Theorems and blow-up arguments.