  In this paper, we extend the method of invariant sets of descending flow that
proposed by Sun Jingxian for smooth functionals to the locally Lipschitz
functionals. By this way, we obtain the existence results for the positive,
negative and sign-changing critical points of the locally Lipschitz
functionals, and apply these theoretical results to the study of differential
inclusion problems with p-Laplacian. In order to obtain the above results,we
develop some new techniques: 1) We establish the method of how to extend the
pseudo-gradient field to the whole space on the premise of preserving the
useful information of the local pseudo-gradient field; 2) In the case of
set-valued mapping, a pseudo-gradient field is established to make both the
cone and the negative cone being invariant sets of descending flow. To obtain
our main results, a new class of (PS) condition is also proposed.
