2-Harmonic Space-like Submanifolds in a Pseudo-Riemannian Space Form

2-Harmonic space-like submanifolds in a pseudo-Riemannian space form was studied,and a Simons form inequality of integration was obtained via calculations.After the submanifold was restricted it became a maximal space-like submanifold,and the Simons form integral inequality was used to discuss the submanifold properties when the sectional curvature of the pseudo-Riemannian space form is positive,negative and zero,respectively,and some results were obtained.