非共振二阶椭圆型方程解存在性的山路引理方法

Mountain pass lemma to a second order elliptic system without resonance

为了研究非共振二阶椭圆型方程解存在性,这里考虑Δ是Laplace算子的情况,注意到算子的特征值问题。首先在每个有限维的步上,应用山路引理,证明了在两个有限维子空间XN,ZN(N=1,2,…)上近似解的存在性,然后推广到(H01(Ω))n空间上证明解的存在性,由此推出具有Dirichlet边界条件的非共振条件二阶椭圆型方程解的存在性。

With the use of variational method,the boundary value of a second order elliptic system without resonance is invastigated,noticing the eigenvalue problem of the Laplace operator,on each finite dimension,the existence of weak solution of the second order elliptic system without resonance by means of Mountain Pass Lemma is firstly proved.Based on it,the problem is proved.