Existence of positive solutions to the nonlinear Choquard equation with competing potentials
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Date
2018-03-07
Authors
Wang, Jun
Qu, Mengmeng
Xiao, Lu
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
This article concerns the existence of positive solutions of the non-linear Choquard equation
-∆u + α(x)u = b(x) (1/|x| ⁎ |u|2)u, u ∈ H1(ℝ3),
where the coefficients α and b are positive functions such that α(x) → κ∞ and b(x) → μ∞ as |x| → ∞. By comparing the decay rate of the coefficients α and b, we prove the existence of positive ground and bound stat solutions of Choquard equation.
Description
Keywords
Positive solutions, Choquard equation, Competing coefficients, Variational methods
Citation
Wang, J., Qu, M., & Xiao, L. (2018). Existence of positive solutions to the nonlinear Choquard equation with competing potentials. <i>Electronic Journal of Differential Equations, 2018</i>(63), pp. 1-21.