Van Schaftingen, Jean
[UCL]
Xia, Jiankang
[UCL]
We consider the nonlinear Choquard equation −Δu+Vu=(Iα∗|u|p)|u|p−2u in ℝN where N≥1, Iα is the Riesz potential integral operator of order α∈(0,N) and p>1. If the potential V∈C(ℝN;[0,+∞)) satisfies the confining condition liminf|x|→+∞V(x)1+|x|N+αp−N=+∞, and 1p>N−2N+α, we show the existence of a groundstate, of an infinite sequence of solutions of unbounded energy and, when p≥2 the existence of least energy nodal solution. The constructions are based on suitable weighted compact embedding theorems. The growth assumption is sharp in view of a Pohožaev identity that we establish.
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Bibliographic reference |
Van Schaftingen, Jean ; Xia, Jiankang. Choquard equations under confining external potentials. In: NoDEA Nonlinear Differential Equations and Applications, Vol. 24, no.1, p. 1–24 (2016) |
Permanent URL |
http://hdl.handle.net/2078.1/179262 |