Journal
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
Volume 52, Issue 1-2, Pages 199-235Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s00526-014-0709-x
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We study the nonlocal equation where , , is the Riesz potential and is a small parameter. We show that if the external potential has a local minimum and then for all small the problem has a family of solutions concentrating to the local minimum of provided that: either , or and , or and . Our assumptions on the decay of and admissible range of are optimal. The proof uses variational methods and a novel nonlocal penalization technique that we develop in this work.
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