Solutions to the nonlinear Schrödinger systems involving the fractional Laplacian
Solutions to the nonlinear Schrödinger systems involving the fractional Laplacian
In this paper, we consider the following nonlinear Schrödinger system involving the fractional Laplacian operator: {(-Δ)α2u+au=f(v),(-Δ)β2v+bv=g(u),on Ω⫅Rn, where a,b≥0 . When Ω is the unit ball or Rn , we prove that the solutions (u,v) are radially symmetric and decreasing. When Ω is the parabolic domain on Rn , we …