Ground states for nonlinear Maxwell-Dirac system with magnetic field

作者：Zhang Jian^*; Tang Xianhua; Zhang Wen

来源：Journal of Mathematical Analysis and Applications, 2015, 421(2): 1573-1586.

DOI：10.1016/j.jmaa.2014.08.009

• Maxwell-Dirac system
• Ground state solutions
• Concentration compactness
• Strongly indefinite functionals

In this paper, we study the following Maxwell-Dirac system with magnetic field and general nonlinearity
{Sigma(3)(k=1)alpha k(-i partial derivative(k) + A(k))u + a beta u +omega u-beta A(0u) = F-u (x,u), -Delta A(0) = 4 pi(beta u)u-4 pi vertical bar u vertical bar(2), -Delta A(k) = 4 pi(alpha(k)u)u, k= 1,2,3,
for x is an element of R-3. Since this problem is strongly indefinite, we use linking and concentration compactness arguments to establish the existence of ground state solutions for this system.

• 单位
  中南大学