Existence of Groundstates for a Class of Nonlinear Choquard Equations in the Plane
(2017) Advanced Nonlinear Studies — Vol. 17, p. 581-594 (2017)
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- Abstract
- We prove the existence of a nontrivial groundstate solution for the class of nonlinear Choquard equation −Δu+u=(Iα∗F(u))F′(u)in ℝ², where Iα is the Riesz potential of order α on the plane ℝ² under general nontriviality, growth and subcriticality on the nonlinearity F∈C¹(ℝ,ℝ).
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Battaglia, L., & Van Schaftingen, J. (2017). Existence of Groundstates for a Class of Nonlinear Choquard Equations in the Plane. Advanced Nonlinear Studies, 17, 581-594. https://doi.org/10.1515/ans-2016-0038 (Original work published 2017)