Advances in Differential Equations

Solutions to upper critical fractional Choquard equations with potential

Xinfu Li, Shiwang Ma, and Guang Zhang

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In this paper, the upper critical fractional Choquard equation is considered. The interest in studying such equation comes from its strong connections with mathematical physics, for example, the fractional quantum mechanics, the Lévy random walk models, and the dynamics of pseudo-relativistic boson stars. Another strong motivation is from some mathematical difficulties such as the coexistence of two fractional diffusions, the lack of compactness, and the attendance of the upper critical exponent. To overcome these difficulties, some methods and techniques need to be combined and a radially symmetric solution is obtained.

Article information

Adv. Differential Equations, Volume 25, Number 3/4 (2020), 135-160.

First available in Project Euclid: 21 March 2020

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J20: Variational methods for second-order elliptic equations 35J60: Nonlinear elliptic equations


Li, Xinfu; Ma, Shiwang; Zhang, Guang. Solutions to upper critical fractional Choquard equations with potential. Adv. Differential Equations 25 (2020), no. 3/4, 135--160.

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