Abstract. In this paper, we consider the biharmonic elliptic systems of the formwhere Ω ⊂ R N is a bounded domain with smooth boundary ∂Ω, ∆ 2 is the biharmonic operator, N ≥ 5, 2 ≤ q < 2 * , 2 * =denotes the critical Sobolev exponent, F ∈ C 1 (R 2 , R + ) is homogeneous function of degree 2 * . By using the variational methods and the Ljusternik-Schnirelmann theory, we obtain multiplicity result of nontrivial solutions under certain hypotheses on λ and δ.
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