Critical point theory for nonsmooth functionals

In this paper, we develop critical point theory for nonsmooth functional f:H01(Ω)→R defined by f(u)=12∫Ω∑i,j=1aij(x,u)DiuDjudx−∫ΩG(x,u)dx. The corresponding deformation lemmas are proved. With the application to the bifurcation for quasilinear Schrödinger equations in mind, we extend the obtained results to that for a functional defined on a product space and prove a generalized saddle point theorem.