Existence of Groundstates for a Class of Nonlinear Choquard Equations in the Plane
Existence of Groundstates for a Class of Nonlinear Choquard Equations in the Plane
复制标题
DOI：
10.1515/ans-2016-0038
复制
发表时间：
2017-08-01
影响因子：
1.8
通讯作者：
Van Schaftingen, Jean
中科院分区：
文献类型：
--
作者：
Battaglia, Luca;Van Schaftingen, Jean
证明了一类非线性Choquard方程-Delta u+u=(i-α*F(U))F‘(U)在R-2中的非平凡基态解的存在性，其中i-α是平面R-2上一般非平凡、增长性和次临界下的Riesz势，F是C-1(R，R)的一个元素.
We prove the existence of a nontrivial groundstate solution for the class of nonlinear Choquard equations-Delta u + u=(I-alpha* F(u))F'(u) in R-2,where I-alpha is the Riesz potential of order alpha on the plane R-2 under general nontriviality, growth and subcriticality on the nonlinearity F is an element of C-1 (R, R).