Classical solutions to a Hartree type system

Phuong Le

Mathematische Nachrichten, 2021, vol. 294, issue 12, 2355-2366

Abstract: This paper is concerned with positive classical solutions to the nonlocal system of Hartree type −Δu=1|x|n−α∗vpvp−1inRn,−Δv=1|x|n−β∗uquq−1inRn,\begin{equation*} \def\eqcellsep{&}\begin{array}{rcl} \hspace*{85pt}-\Delta u &=& \displaystyle {\left(\frac{1}{|x|^{n-\alpha }} * v^p\right)} v^{p-1} \quad \text{ in }\mathbb {R}^n, \hspace*{-85pt}\vspace*{6pt}\\ \hspace*{85pt} -\Delta v &=& \displaystyle {\left(\frac{1}{|x|^{n-\beta }} * u^q\right)} u^{q-1} \quad \text{ in }\mathbb {R}^n, \hspace*{-85pt}\end{array} \end{equation*}where n≥3$n\ge 3$ and 0

Date: 2021
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