Abstract: Variational methods are used to study the nonlinear Schr¨odinger-Poisson type equations which model the electromagnetic wave propagating in the plasma in physics. By analyzing the Hamiltonian property to construct a constrained variational problem, the existence of the ground state of the system is obtained. Furthermore, it is shown that the ground state is orbitally stable.

Key words: Schrödinger-Poisson type equations, ground state, existence, orbital stability