Abstract
In this paper, we establish a compact support principle for a class of elliptic differential inequalities such as Δu⩾C|x| −α ∗ u q for | x| large, where q∈(0,1) and α ∗=(1−q)N+2q is optimal in the sense that it cannot be replaced by any larger number. Applying this principle, we also consider the existence and nonexistence of compact support solutions for a semilinear elliptic equation.
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