TITLE

# Semiclassical stationary states for nonlinear Schrï¿½dinger equations with fast decaying potentials

AUTHOR(S)
Moroz, Vitaly; Van Schaftingen, Jean
PUB. DATE
January 2010
SOURCE
Calculus of Variations & Partial Differential Equations;Jan2010, Vol. 37 Issue 1/2, p1
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
We study the existence of positive solutions for a class of nonlinear Schrï¿½dinger equations of the type where N = 3, p > 1 is subcritical and V is a nonnegative continuous potential. Amongst other results, we prove that if V has a positive local minimum, and $${\frac{N}{N-2} < p < \frac{N+2}{N-2}}$$ , then for small e the problem admits positive solutions which concentrate as e ? 0 around the local minimum point of V. The novelty is that no restriction is imposed on the rate of decay of V. In particular, we cover the case where V is compactly supported.
ACCESSION #
45391242

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