Infinitely many bound states for Choquard equations with local nonlinearities

被引：4
作者：
Li, Xinfu [1 ]
Liu, Xiaonan [2 ,3 ]
Ma, Shiwang [2 ,3 ]
机构：
[1] Tianjin Univ Commerce, Sch Sci, Tianjin 300134, Peoples R China
[2] Nankai Univ, Sch Math Sci, Tianjin 300071, Peoples R China
[3] Nankai Univ, LPMC, Tianjin 300071, Peoples R China
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2019年 / 189卷
基金：
中国国家自然科学基金;
关键词：
Multiplicity; Choquard equations; Bound states; GROUND-STATE; EXISTENCE;
D O I：
10.1016/j.na.2019.111583
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider the following Choquard equation (CH) {-Delta u + u = (I-alpha * vertical bar u vertical bar(p))vertical bar u vertical bar(p-2) u + V(x) vertical bar u vertical bar(q-2) u in R-N, u is an element of H-1(R-N), where N >= 3, alpha is an element of ((N-4)(+), N), p is an element of [2, N+alpha/N-2), q is an element of (2, 2N/N-2) boolean AND(1+ (P -1)(N-2)alpha/N-2, 1+ 2N(N-alpha)+N-2(p-1)/(N-2)alpha) and I-alpha is the Riesz potential. Under some suitable decay assumptions but without any symmetry property on V(x), we prove that the problem has infinitely many solutions, whose energy can be arbitrarily large. (C) 2019 Published by Elsevier Ltd.
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页数：23
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