中文摘要：

我们研究四阶椭圆边值问题 …… 其中ε是一个参数，Ω是R^n中的有界光滑区域,f ∈ C（Ω×R） ,f（x,t）关于t是奇的，且g∈C（Ω×R）．在设有“Ambrosetti—Rabinowitz＇s超二次条件”下，用对称型山路理论获得问题一的无穷多解．此外，对厂施加适当条件，我们能证明：对任意J∈N，存在εj〉0，使得如果｜ε｜≤εj，则第二个问题至少有j个不同的解．关键词：扰动；对称；椭圆边值问题；多重解

英文摘要：

We consider the multiplicity of solutions for the fourth-order elliptic problems …… where ε is a parameter, Ω2 is a smooth bounded domain in R^N ,f ∈ C（Ω×R） ,f（x,t） is odd with respect to t, and g ∈ C（Ω × R）. Using symmetric mountain pass theorem and analytic technique we obtain infinitely many solutions for the first problem under no Ambrosetti-Rabinowitz＇s superquadratic condition. Moreover, under suitable conditions only on f, we prove that for any j ∈ N there exists εj 〉 0 such that if ｜ε｜ ∈εj, then the above second problem possesses at least j distinct solutions.