Critical point theory for nonsmooth functionals Original Research Article

In this paper, we develop critical point theory for nonsmooth functional View the MathML sourcef:H01(Ω)→R defined by View the MathML sourcef(u)=12∫Ω∑i,j=1aij(x,u)DiuDjudx−∫ΩG(x,u)dx. Turn MathJax on 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.