Recent Progress in Supercritical Elliptic Problems
نویسنده
چکیده
We consider the elliptic problem ∆u+up = 0, u > 0 in an exterior domain, Ω = RN \D under zero Dirichlet and vanishing conditions, where D is smooth and bounded, and p is supercritical, namely p > N+2 N−2 . We prove that the associated Dirichlet problem has infinitely many positive solutions with slow decay O(|x| 2 p−1 ) at infinity. In addition, a fast decay solution exists if p is close enough to the critical exponent. If p differs from certain sequence of resonant values which tends to infinity, then the Dirichlet problem is also solvabe in a bounded domain Ω with a sufficiently small spherical hole.
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