Nodal solutions for pseudo-relativistic Hartree equations

被引：1

作者：

Huang, Zhihua ^{[1
]}

Yang, Jianfu ^{[2
]}

Yu, Weilin ^{[3
]}

机构：

[1] Guangdong Univ Educ, Dept Math, Guangzhou 510310, Guangdong, Peoples R China

[2] Jiangxi Normal Univ, Dept Math, Nanchang 330022, Jiangxi, Peoples R China

[3] Chinese Acad Sci, Inst Appl Math, AMSS, Beijing 100190, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2021年 / 493卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Hartree equations; Nodal solutions; Extension method; Constrained problem; FRACTIONAL LAPLACIAN; ELLIPTIC PROBLEM; GROUND-STATES; EXISTENCE;

D O I：

10.1016/j.jmaa.2020.124474

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we investigate the existence of nodal solutions for the following problem (P-0) (-Delta + m(2))(alpha) u = (vertical bar x vertical bar(-mu) *vertical bar u vertical bar(p))vertical bar u|vertical bar(p-2)u, in R-N, where 1/2 < alpha < 1, 0 < mu <= 2 and 2N-mu/n-1 < p < 2N-mu/N-2 alpha . We show that for any positive integer k, problem (P-0) possesses a radially symmetrical solution changing sign exactly k-times. (c) 2020 Elsevier Inc. All rights reserved.

引用

页数：18

共 23 条

[1] [Anonymous], 2017, COMPLEXITY
[2] Applebaum D., 2004, NOT AM MATH SOC, V51, P1336
[3] On some critical problems for the fractional Laplacian operator
Barrios, B.
Colorado, E.
de Pablo, A.
Sanchez, U.
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2012, 252 (11) : 6133 - 6162
[4] INFINITELY MANY RADIAL SOLUTIONS OF A SEMILINEAR ELLIPTIC PROBLEM ON R(N)
BARTSCH, T
WILLEM, M
[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1993, 124 (03) : 261 - 276
[5] Belchior P., ARXIV180203963V1
[6] A concave-convex elliptic problem involving the fractional Laplacian
Braendle, C.
Colorado, E.
de Pablo, A.
Sanchez, U.
[J]. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2013, 143 (01) : 39 - 71
[7] Bueno H., ARXIV180511985V1
[8] Positive solutions of nonlinear problems involving the square root of the Laplacian
Cabre, Xavier
Tan, Jinggang
[J]. ADVANCES IN MATHEMATICS, 2010, 224 (05) : 2052 - 2093
[9] An extension problem related to the fractional Laplacian
Caffarelli, Luis
Silvestre, Luis
[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2007, 32 (7-9) : 1245 - 1260
[10] ON THE EXISTENCE AND NODAL CHARACTER OF SOLUTIONS OF SEMILINEAR ELLIPTIC-EQUATIONS
CAO, DM
ZHU, XP
[J]. ACTA MATHEMATICA SCIENTIA, 1988, 8 (03) : 345 - 359

← 1 2 3 →