Ground state of a magnetic nonlinear Choquard equation.
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Date
2019
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Abstract
We consider the stationary magnetic nonlinear Choquard equation −(∇ + iA(x))2u + V(x)u = (1|x|α ∗ (|u|)
) f(|u|) |u| u, where A : RN → RN is a vector potential, V is a scalar potential, f : R → R and
F is the primitive of f . Under mild hypotheses, we prove the existence of a ground state solution for this problem. We also prove a simple multiplicity result by applying Ljusternik–Schnirelmann methods.
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Keywords
Variational methods, Splitting lemma
Citation
BUENO, H.; MAMANI, G. G.; PEREIRA, G. de A. Ground state of a magnetic nonlinear Choquard equation. Nonlinear Analysis-Theory Methods & Applications, v. 181, p. 189-199, 2019. Disponível em: <https://www.sciencedirect.com/science/article/pii/S0362546X18302967>. Acesso em: 06 jul. 2022.