Journal
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
Volume 161, Issue -, Pages 87-107Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.na.2017.05.014
Keywords
Nonlinear Choquard equations; Nonlocal semilinear elliptic equation; Semi-classical limit; Variational methods
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Funding
- Projet de Recherche (Fonds de la Recherche Scientifique-FNRS) Existence and asymptotic behavior of solutions to systems of semilinear elliptic partial differential equations [T.1110.14]
- NSF of China [NSFC-11271201]
- China Scholarship Council
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We study the nonlocal Choquard equation -epsilon(2) Delta u(epsilon) + Vu(epsilon) = (I-alpha *|u(epsilon)|(p))|u(epsilon)|(p-2)u(epsilon) in R-N where N >= 1,I-alpha is the Riesz potential of order alpha is an element of (0, N) and epsilon > 0 is a parameter. When the nonnegative potential V is an element of C(R-N) achieves 0 with a homogeneous behavior or on the closure of an open set but remains bounded away from 0 at infinity, we show the existence of groundstate solutions for small epsilon > 0 and exhibit the concentration behavior as epsilon -> 0. (C) 2017 Elsevier Ltd. All rights reserved.
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