Multiple positive solutions of elliptic systems in exterior domains

Abstract

In this paper, existence and multiplicity of positive solutions of the elliptic system [Formula: see text] is proved, where [Formula: see text] is an exterior domain in [Formula: see text] such that [Formula: see text] is far away from the origin and contains a sufficiently large ball, [Formula: see text], and the coefficients [Formula: see text] are continuous functions on [Formula: see text] which tend to positive constants at infinity. We do not assume [Formula: see text] to be positive functions.