ON SOME QUALITATIVE ASPECTS FOR DOUBLY NONLOCAL EQUATIONS

SILVIA CINGOLANI; MARCO GALLO

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ON SOME QUALITATIVE ASPECTS FOR DOUBLY NONLOCAL EQUATIONS

机译：ON SOME QUALITATIVE ASPECTS FOR DOUBLY NONLOCAL EQUATIONS

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In this paper we investigate some qualitative properties of thesolutions to the following doubly nonlocal equation ( -Δ )~su + μu = (I_α * F(u))F'(u) in RN （P）where N≥2, ∈2 (0; 1),α∈(0;N), μ > 0is fixed, ( -Δ )~s denotes the fractional Laplacian and I_α is the Riesz potential. Here F ∈ C~1（R）stands fora general nonlinearity of Berestycki-Lions type. We obtain rst some regularityresult for the solutions of (P). Then, by assuming F odd or even and positiveon the half-line, we get constant sign and radial symmetry of the Pohozaevground state solutions related to equation (P). In particular, we extend someresults contained in [23]. Similar qualitative properties of the ground statesare obtained in the limiting case s = 1, generalizing some results by Moroz andVan Schaftingen in [52] when F is odd.

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《Discrete and continuous dynamical systems, Series S》 |2022年第12期|3603-3620|共18页
作者
SILVIA CINGOLANI; MARCO GALLO;
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作者单位

Dipartimento di MatematicaUniversita degli Studi di Bari Aldo MoroVia E. Orabona 4, 70125 Bari, Italy;

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Nonlinear Schrodinger equation; double nonlocality; Choquard equations; Hartree type term; fractional Laplacian; qualitative properties of the solutions; regularity; sign of the ground states; positivity; radial symmetry;

ON SOME QUALITATIVE ASPECTS FOR DOUBLY NONLOCAL EQUATIONS

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