An Abstract Critical Point Theorem and Applications

In this paper,we prove a following critical point theorem by using linkmethod in [1]. Theorem 1.1. Let X be a real Banach space,X_1,X_2 be subspaces of X.X=X_1+X_2 and dim X_2=m<+∞,f(x)∈ C~1(X,R)satisfies Palais-Smale conditionand following three conditions: i)There exist ρ>0,β>a such that f|βρηx_1≥β, ii)There exist e∈β_R∩X_1,R>ρ such that