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Infinitely many non-radial solutions for a Choquard equation
Advances in Nonlinear Analysis ( IF 3.2 ) Pub Date : 2022-03-09 , DOI: 10.1515/anona-2022-0224
Fashun Gao 1 , Minbo Yang 2
Affiliation  

In this article, we consider the non-linear Choquard equation Δ u + V ( x ) u = R 3 u ( y ) 2 x y d y u in R 3 , -\Delta u+V\left(| x| )u=\left(\mathop{\int }\limits_{{{\mathbb{R}}}^{3}}\frac{| u(y){| }^{2}}{| x-y| }{\rm{d}}y\right)u\hspace{1.0em}\hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0.33em}{{\mathbb{R}}}^{3}, where V ( r ) V\left(r) is a positive bounded function. Under some proper assumptions on V ( r ) V\left(r) , we are able to establish the existence of infinitely many non-radial solutions.

中文翻译:

Choquard 方程的无穷多个非径向解

在本文中,我们考虑非线性 Choquard 方程 - Δ + ( X ) = R 3 ( 是的 ) 2 X - 是的 d 是的 R 3 , -\Delta u+V\left(| x| )u=\left(\mathop{\int }\limits_{{{\mathbb{R}}}^{3}}\frac{| u(y){ | }^{2}}{| xy| }{\rm{d}}y\right)u\hspace{1.0em}\hspace{0.1em}\text{in}\hspace{0.1em}\hspace{ 0.33em}{{\mathbb{R}}}^{3}, 在哪里 ( r ) V\左(r) 是一个正有界函数。在一些适当的假设下 ( r ) V\左(r) ,我们能够建立无限多个非径向解的存在性。
更新日期:2022-03-09
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