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

Abstract:

Let 1 < p < N, and u be a nonnegative solution of - Δ<inf>p</inf> u = f (x, u) on R^N {set minus} over(B<inf>1</inf>, -) where f behaves like | x |^{- l} u^q near | x | = ∞ and u = 0, for some constants q ≥ 0 and l ∈ 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 - Δ<inf>p</inf> u = f (x, v), - Δ<inf>p</inf> 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-Véron and Pohozaev, and other authors. Our proofs use tools such as Harnack inequality, the Maximum Principle, Liouville Theorems and blow-up arguments. © 2008.

Año de publicación:

2008

Keywords:

• Entire solution
• Nonlinear elliptic equation
• p-Laplace
• Asymptotics
• Nonlinear System

Fuente:

scopus