Least action nodal solutions for the quadratic Choquard equation
(2017) Proceedings of the American Mathematical Society — Vol. 145, n° 2, p. 737-747 (2016)
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- Abstract
- We prove the existence of a minimal action nodal solution for the quadratic Choquard equation −Δu+u=(Iα∗|u|2)u in ℝN, where Iα is the Riesz potential of order α∈(0,N). The solution is constructed as the limit of minimal action nodal solutions for the nonlinear Choquard equations −Δu+u=(Iα∗|u|p)|u|p−2u in ℝN when p↘2. The existence of minimal action nodal solutions for p>2 can be proved using a variational minimax procedure over Nehari nodal set. No minimal action nodal solutions exist when p<2.
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Citations
Ghimenti, M., Moroz, V., & Van Schaftingen, J. (2017). Least action nodal solutions for the quadratic Choquard equation. Proceedings of the American Mathematical Society, 145(2), 737-747. https://doi.org/10.1090/proc/13247 (Original work published 2016)