A Liouville-type theorem for semilinear elliptic systems via moving spheres

Yajing Zhang

Vol. 236 (2008), No. 2, 389–396

DOI: 10.2140/pjm.2008.236.389

Abstract

In this paper, we consider second order semilinear elliptic systems of the form −Δu = a(x)v^p and −Δv = b(x)u^q in ℝ^N for N ≥ 3, where p,q > 0 and a,b ∈ C(ℝ^N). We prove a new Liouville-type theorem for the system under appropriate conditions on the nonlinearity.

Keywords

positive solution, Liouville-type theorem, moving spheres

Mathematical Subject Classification 2000

Primary: 35J60

Secondary: 35J45

Milestones

Received: 21 September 2007

Revised: 16 March 2008

Accepted: 30 April 2008

Published: 1 June 2008