Abstract
This paper is devoted to the study of positive solutions of the semilinear elliptic equation Δ u + K ( | x | ) u − p = 0 , x ∈ R n with n ⩾ 3 and p > 0 . Asymptotic behaviours of sky states and uniqueness of singular sky states are obtained via invariant manifold theory of dynamical systems. The Dirichlet problem in exterior domains is also studied. It is proved that this problem has infinitely many positive solutions with fast growth.
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