Abstract
In this article, the existence of non-negative solution to a perturbed conformal invariant integral equation was studied. As <italic>p</italic>∈ (-<italic>n</italic>; 0); <italic>q</italic> > 0 such that <italic>pq</italic> + <italic>p</italic> + 2<italic>n</italic> = 0, the existence of non-negative solutions to perturbed integral equation is established, however as <italic>p</italic> ∈ (0;∞); <italic>q</italic> < 0 such that <italic>pq</italic> + <italic>p</italic> + 2<italic>n</italic> = 0, we show the perturbed integral equation has not non-negative solutions, which is different from the original conformal invariant integral equation and denotes the existence of integral equation is determined by the behavior of solution near infinity.
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