| 一类退缩椭圆方程组的特征值问题 |
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| 引用本文： | 张公敬.一类退缩椭圆方程组的特征值问题[J].青岛科技大学学报,1997(1). |
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| 作者姓名： | 张公敬 |
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| 作者单位： | 青岛大学计算机系 |
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| 摘 要： | 设ΩＲ＋ｎ＝｛Ｘ＝（ｘ１，ｘ２，…ｘＮ）｜ｘ１＞０，Ｎ＞３｝为有界光滑区域，Ｒ＋Ｎ∩Ω≠Φ。文中利用临界点理论，讨论退缩椭圆型方程组Ｔｕｋ≡－∑Ｎｉ＝１Ｄｉ（ｘｉａＤｉｕｋ）＝λｆｋ（ｘ，ｕ１，ｕ２，…ｕｎ），ｉｎΩｕｋ＝０ｏｎΩ，ｋ＝１，２，…ｎ｛非平凡广义解的存在性。
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| 关 键 词： | 退缩椭圆方程组 临界点 广义解 |
Nonlinear Eigenvalue Problem For a Group of Degenerate Elliptic Equation Systems |
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| Zhang Gong jing.Nonlinear Eigenvalue Problem For a Group of Degenerate Elliptic Equation Systems[J].Journal of Qingdao University of Science and Technology:Natutral Science Edition,1997(1). |
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| Authors: | Zhang Gong jing |
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| Abstract: | Let Ω be a bounded domain in R N +={x=(x 1,x 2,…x N)|x 1>0,N>3} with a smooth boundery Ω(Ω∩R N +≠Φ).The question is discussed that the existence of nontrivial solutions of the degenerate elliptic equation systems Tu k≡-Ni=1D i(x a 1D iu k)=λf k(x,u 1,u 2,···u n) in Ω u k=0 on Ω where a>0 and T is a degenerate elliptic operator. |
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| Keywords: | degenerate elliptic equation systems critical point weakly solution |
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