Journal
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
Volume 164, Issue -, Pages 38-53Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.na.2017.08.005
Keywords
Variational methods; Polynomial decay; Fractional Laplacian; Choquard equations
Categories
Funding
- CNPq/Brazil [304015/2014-8]
- INCTMAT/CNPQ/Brazil
- CAPES/Brazil
- PNPD/CAPES/Brazil
- CNPq/Brazil [304015/2014-8]
- INCTMAT/CNPQ/Brazil
- CAPES/Brazil
- PNPD/CAPES/Brazil
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With appropriate hypotheses on the nonlinearity f, we prove the existence of a ground state solution u for the problem {(- Delta(p))(s)u + A vertical bar u vertical bar(p-2) u = (1/vertical bar x vertical bar(mu) * F(u)) f(u) in R-N, where 0 < mu < N, (-Delta(p))(s) stands for the (s, p)-Laplacian operator, F is the primitive of f and A is a positive constant. When mu < p, we also show that u is an element of L-infinity (R-N) boolean AND C-0 (R-N) and has polynomial decay. (C) 2017 Elsevier Ltd. All rights reserved.
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