Existence and asymptotic behaviour of the least energy solutions for a quasilinear Dirac-Poisson system

In the present paper, we study the existence and asymptotic behaviour of solutions of a quasilinear Dirac-Poisson system, α 3 and β are 4 × 4 Pauli-Dirac matrices, a > 0 is a constant, the operator ∆ 4 is the 4-Laplacian, defined as ∆ 4 φ := div(|∇φ| 2 ∇φ).By applying the variational argument, we establish the existence result of least energy solutions and obtain the regularity and the exponential decay estimate.Furthermore, we also prove that the least energy solutions of the quasilinear Dirac-Poisson system converge to a solution of the limit Dirac-Maxwell system.k=1 α k ∂ k and