Nodal solutions for the Choquard equation
(2016) Journal of Functional Analysis — Vol. 271, n° 1, p. 107-135 (2016)
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- Abstract
- We consider the general Choquard equations −Δu+u=(Iα∗|u|^p)|u|^(p−2)u where Iα is a Riesz potential. We construct minimal action odd solutions for p∈((N+α)/N,(N+α)/(N−2)) and minimal action nodal solutions for p∈(2,(N+α)/(N−2)). We introduce a new minimax principle for least action nodal solutions and we develop new concentration-compactness lemmas for sign-changing Palais-Smale sequences. The nonlinear Schrödinger equation, which is the nonlocal counterpart of the Choquard equation, does not have such solutions.
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Citations
Ghimenti, M., & Van Schaftingen, J. (2016). Nodal solutions for the Choquard equation. Journal of Functional Analysis, 271(1), 107-135. https://doi.org/10.1016/j.jfa.2016.04.019 (Original work published 2016)