Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 475, Issue 2, Pages 1685-1713Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2019.03.039
Keywords
Choquard equation; Critical exponential growth; Trudinger-Moser inequality
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Funding
- NSFC [11571317]
- ZJNSF [LD19A010001]
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In this paper we are interested in the following nonlocal nonhomogeneous elliptic equation in R-2, -Delta V(x)u = (1/vertical bar x vertical bar(mu) * F(u)/ vertical bar x vertical bar(beta)) f(u)/vertical bar x vertical bar(beta) + epsilon h(x) in R-2, where V is a positive continuous potential, 0 < mu < 2, beta > 0, 2 beta, mu <= 2, epsilon is a small parameter and F(s) is the primitive function of f(8). Suppose that the nonlinearity f (s) is of critical exponential growth in the sense of Trudinger-Moser inequality, we prove the existence and multiplicity of solutions by variational methods. (C) 2019 Elsevier Inc. All rights reserved.
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