Journal
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
Volume 66, Issue 6, Pages 3049-3060Publisher
SPRINGER INTERNATIONAL PUBLISHING AG
DOI: 10.1007/s00033-015-0565-3
Keywords
Nonlinear Schrodinger equations; Standing waves; Variational methods; Critical growth; Trudinger-Moser inequalities; Lack of compactness; Unbounded domains
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Funding
- National Institute of Science and Technology of Mathematics ICNT-Mat
- CAPES
- CNPq/Brazil
- CAPES/Brazil
- CPSF [2013M530868]
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In this paper, we deal with the following singularly perturbed elliptic problem -epsilon(2) Delta u + V(x)u = f(u), u is an element of H-1(R-2), where f(s) has critical growth of Trudinger-Moser type. In this paper, we construct a localized bound-state solution concentrating at an isolated component of the positive local minimum points of V as epsilon -> 0 under certain conditions on f(s). Our results complete the analysis made in Byeon et al. (Commun Partial Differ Equ 33: 1113-1136, 2008) for the two-dimensional case, in the sense that, in that paper only the subcritical growth was considered.
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