Journal
ADVANCED NONLINEAR STUDIES
Volume 16, Issue 4, Pages 843-861Publisher
WALTER DE GRUYTER GMBH
DOI: 10.1515/ans-2016-0097
Keywords
Trudinger-Moser Inequality; Nonlinear Schrodinger Equations; Variational Methods; Mountain Pass Theorem; Lack of Compactness; Critical Growth; Trudinger-Moser Inequality; Fractional Laplacian
Categories
Funding
- INCTMAT/CNPq/Brazil
- CNPq/Brazil [304036/2013-7, 407099/2013-1, 304015/2014-8]
- CAPES/Brazil [2531/14-3]
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In this paper, we deal with the singular perturbed fractional elliptic problem is an element of(-Delta)(1/2)u + V(z)u = f(u) in IR, where (-Delta)(1/)2u is the square root of the Laplacian and f(s) has exponential critical growth. Under suitable conditions on f(s), we construct a localized bound state solution concentrating at an isolated component of the positive local minimum points of the potential of V as epsilon goes to 0.
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