Existence of nontrivial solutions for a perturbation of Choquard equation with Hardy-Littlewood-Sobolev upper critical exponent
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Date
2018-06-15
Authors
Su, Yu
Chen, Haibo
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this article, we consider the problem
-∆u = (∫ℝN |u|2*μ/|x - y|μ dy) |u|2*μ - 2 u + ƒ(x, u) in ℝN,
where N ≥ 3, μ ∈ (0, N) and 2*μ = 2N - μ/N - 2. Under suitable assumptions on ƒ(x, u), we establish the existence and non-existence of nontrivial solutions via the variational method.
Description
Keywords
Hardy-Littlewood-Sobolev upper critical exponent, Choquard equation
Citation
Su, Y., & Chen, H. (2018). Existence of nontrivial solutions for a perturbation of Choquard equation with Hardy-Littlewood-Sobolev upper critical exponent. <i>Electronic Journal of Differential Equations, 2018</i>(123), pp. 1-25.
Rights
Attribution 4.0 International