@article{5f01d67fcc4743afae1c40a0b74b0cda,
title = "Multiplicity of radial and nonradial solutions to equations with fractional operators",
abstract = "In this paper, we study the existence of radial and nonradial solutions to the scalar field equations with fractional operators. For radial solutions, we prove the existence of infinitely many solutions under N ≥ 2. We also show the existence of least energy solution (with the Pohozaev identity) and its mountain pass characterization. For nonradial solutions, we prove the existence of at least one nonradial solution under N ≥ 4 and infinitely many nonradial solutions under either N = 4 or N ≥ 6. We treat both of the zero mass and the positive mass cases.",
keywords = "Nonradial solutions, Positive mass case, Radial solutions, Symmetric mountain pass thoerem, Zero mass case",
author = "Norihisa Ikoma",
note = "Funding Information: 2010 Mathematics Subject Classification. Primary: 35J20, 35J60. Key words and phrases. Radial solutions, nonradial solutions, symmetric mountain pass tho-erem, zero mass case, positive mass case. The author is supported by JSPS KAKENHI Grant Number JP16K17623 and JP17H02851. Publisher Copyright: {\textcopyright} 2020 American Institute of Mathematical Sciences. All rights reserved.",
year = "2020",
month = jul,
doi = "10.3934/CPAA.2020153",
language = "English",
volume = "19",
pages = "3501--3530",
journal = "Communications on Pure and Applied Analysis",
issn = "1534-0392",
publisher = "American Institute of Mathematical Sciences",
number = "7",
}