We are interested in a general Choquard equation [Formula presented] under suitable assumptions on the bounded potential V and on the nonlinearity f. Our analysis extends recent results by the second and third author on the problem with μ=0 and pure-power nonlinearity f(x,u)=|u|p−2u. We show that, under appropriate assumptions on the potential, whether the ground state does exist or not. Finally, we study the asymptotic behaviour of ground states as μ→0+.

Bernini, F., Bieganowski, B., Secchi, S. (2022). Semirelativistic Choquard equations with singular potentials and general nonlinearities arising from Hartree–Fock theory. NONLINEAR ANALYSIS, 217(April 2022) [10.1016/j.na.2021.112738].

Semirelativistic Choquard equations with singular potentials and general nonlinearities arising from Hartree–Fock theory

Bernini F.
;
Secchi S.
2022

Abstract

We are interested in a general Choquard equation [Formula presented] under suitable assumptions on the bounded potential V and on the nonlinearity f. Our analysis extends recent results by the second and third author on the problem with μ=0 and pure-power nonlinearity f(x,u)=|u|p−2u. We show that, under appropriate assumptions on the potential, whether the ground state does exist or not. Finally, we study the asymptotic behaviour of ground states as μ→0+.
Articolo in rivista - Articolo scientifico
Choquard equation; Fractional operators; Hartree–Fock theory; Sign-changing nonlinearities;
English
Bernini, F., Bieganowski, B., Secchi, S. (2022). Semirelativistic Choquard equations with singular potentials and general nonlinearities arising from Hartree–Fock theory. NONLINEAR ANALYSIS, 217(April 2022) [10.1016/j.na.2021.112738].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/346842
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