Groundstates for a local nonlinear perturbation of the Choquard equations with lower critical exponent

Van Schaftingen, Jean;Xia, Jiankang
(2018) Journal of Mathematical Analysis and Applications — Vol. 464, n° 2, p. 1184-1202 (2018)

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  • Van Schaftingen, Jeanorcid-logoUCLouvain
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  • Xia, Jiankangorcid-logoNorthwestern Polytechnical University, Xi'an, China
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Abstract
We prove the existence of ground state solutions by variational methods to the nonlinear Choquard equations with a nonlinear perturbation −Δu+u=(I_α ∗|u|^(α/N+1))|u|^(α/N−1)u + f (x,u) in R^N where N≥1, I_α is the Riesz potential of order α∈(0,N), the exponent α/N+1 is critical with respect to the Hardy—Littlewood—Sobolev inequality and the nonlinear perturbation f satisfies suitable growth and structural assumptions.
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Van Schaftingen, J., & Xia, J. (2018). Groundstates for a local nonlinear perturbation of the Choquard equations with lower critical exponent. Journal of Mathematical Analysis and Applications, 464(2), 1184-1202. https://doi.org/10.1016/j.jmaa.2018.04.047 (Original work published 2018)