  In this paper, some existence results for sign-changing critical points of
locally Lipschitz functionals in real Banach space are obtained by the method
combining the invariant sets of descending ow method with a quantitative
deformation. First we assume the locally Lipschitz functionals to be outwardly
directed on the the boundary of some closed convex sets of the real Banach
space. By using the relation between the critical points on the Banach space
and those of the closed convex sets, we construct a quantitative deformation
lemma, and then we obtain some linking type of critical points theorems. These
theoretical results can be applied to the study of the existence of
sign-changing solutions for differential inclusion problems. In contrast with
the related results in the literatures, the main results of this paper relax
the requirement that the functional being of C1 continuous to locally
Lipschitz.
