四阶椭圆边值问题的对称扰动(英文)

Perturbations from Symmetric Fourth Elliptic BoundaryValue Problems

我们研究四阶椭圆边值问题其中ε是一个参数,Ω是RN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f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.

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.