Vol. 317, No. 1, 2022

 Recent Issues Vol. 317: 1 Vol. 316: 1  2 Vol. 315: 1  2 Vol. 314: 1  2 Vol. 313: 1  2 Vol. 312: 1  2 Vol. 311: 1  2 Vol. 310: 1  2 Online Archive Volume: Issue:
 The Journal Subscriptions Editorial Board Officers Contacts Submission Guidelines Submission Form Policies for Authors ISSN: 1945-5844 (e-only) ISSN: 0030-8730 (print) Special Issues Author Index To Appear Other MSP Journals
Regularity, symmetry and asymptotic behaviour of solutions for some Stein–Weiss-type integral systems

Michael Melgaard, Minbo Yang and Xianmei Zhou

Vol. 317 (2022), No. 1, 153–186
Abstract

We consider the positive solutions of some integral systems related to the static Hartree-type equations:

where $N\ge 3$, $p\ge 1$, $0<\mu ,\tau , $\alpha ,\beta \ge 0$ and $0<\alpha +\beta +\mu \le N$. Firstly, assuming that the exponent $p$ belongs to some suitable interval depending on the parameters $\mu ,\tau ,\alpha ,\beta$, we are able to prove some nonexistence results for the positive solution. Secondly, we also establish some qualitative results for the integrable solution of the system like regularity, symmetry and asymptotic behaviour. As a corollary, we deduce the corresponding results for the equivalent weighted Hartree-type nonlocal equations. The results obtained in this paper generalise and complement the existing results in the literature.

Keywords
integral systems, weighted Hartree equation, Riesz potential, integrable solution, decay rate
Primary: 35J15
Secondary: 45G05