| 非共振二阶椭圆型方程解存在性的山路引理方法 |
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| 引用本文： | 潘建丹.非共振二阶椭圆型方程解存在性的山路引理方法[J].阜阳师范学院学报(自然科学版),2010,27(4). |
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| 作者姓名： | 潘建丹 |
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| 作者单位： | 温州大学城市学院,基础教学部,浙江,温州,325035 |
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| 摘 要： | 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。
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| 关 键 词： | 非共振条件 临界点 P.S.条件 山路引理 弱解 |
Mountain pass lemma to a second order elliptic system without resonance |
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| PAN Jian-dan.Mountain pass lemma to a second order elliptic system without resonance[J].Journal of Fuyang Teachers College:Natural Science,2010,27(4). |
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| Authors: | PAN Jian-dan |
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| Institution: | PAN Jian-dan(City School of Wenzhou University,Wenzhou Zhejiang 325035,China) |
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| Abstract: | 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. |
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| Keywords: | non-resonance critical point P S condition Mountain Pass Lemma weak solution |
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