Minimax and Multiplicity Results

Using the deformation lemmas from the previous chapter, various existence and multiplicity results concerning the critical points for nonsmooth functionals are provided in this chapter. We start with the Mountain Pass, Saddle Point and Linking theorems for locally Lipschitz functions which satisfy the generalized (φ − C)c condition. The “zero altitude case” and the symmetric version of the Mountain Pass Theorem are also discussed. Finally, minimax results for Szulkin functionals and some Schecter-type as well as Ricceri-type multiplicity results are given.