Existence of solutions for a nonlinear Choquard equation with potential vanishing at infinity
Existence of solutions for a nonlinear Choquard equation with potential vanishing at infinity
复制标题
无穷远势为零的非线性 Choquard 方程解的存在性
DOI：
10.1515/anona-2015-0123
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发表时间：
2016-11-01
影响因子：
4.2
通讯作者：
Yang, Minbo
中科院分区：
文献类型：
--
作者：
Alves, Claudianor O.;Figueiredo, Giovany M.;Yang, Minbo
研究如下非线性Choquard方程：-Delta u+V(X)u=1/|x|(U)*F(U))f(U)在R-n中，其中0<；u<；N，N>；=3，V是连续实函数，F是f的本原函数.在势V的适当假设下，包括V(无穷)=0，即V(X)->；0为|x|->；+无穷，我们用惩罚的方法证明了上述方程的非平凡解的存在性.
We study the following nonlinear Choquard equation:-Delta u + V(x)u = 1/|x|(u) * F(u) )f(u) in R-n,where 0 < mu < N, N >= 3, V is a continuous real function and F is the primitive function of f. Under some suitable assumptions on the potential V, which include the case V(infinity) = 0, that is, V( x) -> 0 as |x| -> +infinity, we prove the existence of a nontrivial solution for the above equation by the penalization method.