论文标题
球上choquard型方程的阳性基态溶液的独特性，对称性和收敛性
Uniqueness, symmetry and convergence of positive ground state solutions of the Choquard type equation on a ball
论文作者
论文摘要
本文关注的是BALL $ B_R $上非本地Choquard Type方程的积极基态解决方案的定性属性。首先，我们通过使用Talenti的不平等现象证明了积极基础状态解决方案的径向对称性。接下来，我们开发牛顿定理，然后求助于收缩原则，以确立积极基础解决方案的独特性。最后，通过构建截止功能并应用能量比较方法，我们将正态解决方案的融合为$ r \ to \ infty $。我们的结果概括并改善了文献中现有的结果。
This paper is concerned with the qualitative properties of the positive ground state solutions to the nonlocal Choquard type equation on a ball $B_R$. First, we prove the radial symmetry of the positive ground state solutions by using Talenti's inequality. Next we develop Newton's Theorem and then resort to the contraction mapping principle to establish the uniqueness of the positive ground state solutions. Finally, by constructing cut-off functions and applying energy comparison method, we show the convergence of the positive ground state solutions as $R\to \infty$. Our results generalize and improve the existing ones in the literature.
