We discuss the existence of ground state solutions for the Choquard equation-Δu + u-(Iα←F(u)) F'(u) inℝN. We prove the existence of solutions under general hypotheses, investigating in particular the case of a homogeneous nonlinearity F(u) =|u|p/p. The cases N = 2 and N ≥ 3 are treated differently in some steps. The solutions are found through a variational mountain-pass strategy. The results presented are contained in the papers [8, 2].
Battaglia, L. (2016). Ground state solutions fora nonlinear Choquard equation. RENDICONTI DEL SEMINARIO MATEMATICO, 74(3-4), 53-60.
Ground state solutions fora nonlinear Choquard equation
Battaglia, L.
2016-01-01
Abstract
We discuss the existence of ground state solutions for the Choquard equation-Δu + u-(Iα←F(u)) F'(u) inℝN. We prove the existence of solutions under general hypotheses, investigating in particular the case of a homogeneous nonlinearity F(u) =|u|p/p. The cases N = 2 and N ≥ 3 are treated differently in some steps. The solutions are found through a variational mountain-pass strategy. The results presented are contained in the papers [8, 2].File in questo prodotto:
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