Gonzalez, M. and Monneau, R. (2012) Slow Motion of Particle Systems as a Limit of a Reaction-Diffusion Equation with Half-Laplacian in Dimension One. Discrete and Continuous Dynamical Systems, 32, 1255-1286.
https://doi.org/10.3934/dcds.2012.32.1255

has been cited by the following article:

• TITLE: Semilinear Fractional Elliptic Equation of Normal Solution

  AUTHORS: Tao Li

  KEYWORDS: Fractional Laplacian, Variational Method, Semilinear

  JOURNAL NAME: Open Access Library Journal, Vol.11 No.4, March 29, 2024

  ABSTRACT: In this paper, a semilinear elliptic equation of fractional order is constructed by combining the semilinear elliptic equation with the fractional order equation. On this basis, the “standardized” solution, which is often sought by physicists, is studied. In order to overcome the problem of lack of boundness, we set up appropriate conditions to prove the existence of the solution by means of variational theorem and the mountain road theorem.