Abstract: With the help of the Mountain-Pass Theorem lacking Palais-Smale compactness condition and by adoption of the best attained function of Sobolev embedding, the paper sucessfully ovetcomes seria1 difficulties caused by lose of compactness due to Sobolev embedding and proves the existence of nontrivial solutions of two classes of critical biharmonic equations on boundary conditions.

Key words: (PS)c condition, Mountain-Pass theorem, Best embedding constant, Biharmonic equations