| 一类拟线性椭圆方程组非平凡解的存在性 |
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| 引用本文： | 章国庆,刘三阳.一类拟线性椭圆方程组非平凡解的存在性[J].高校应用数学学报(A辑),2004,19(3):297-302. |
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| 作者姓名： | 章国庆 刘三阳 |
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| 作者单位： | 西安电子科技大学,应用数学系,陕西西安,710071;上海理工大学 理学院,上海,200093;西安电子科技大学,应用数学系,陕西西安,710071 |
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| 基金项目： | 教育部跨世纪优秀人才基金(2003年) |
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| 摘 要： | 首先证明了一个抽象的紧性定理，然后借此定理证明了对应于一类拟线性椭圆方程组的泛函在比Boccardo和De．Figueiredo(2002)的条件更弱的条件(文中记为弱类(AR)条件)下满足(C)条件，并利用山路引理证明了这类拟线性椭圆方程组非平凡解的存在性，最后举出两个例子验证了文中所给条件(即弱类(AR)条件)的确比Boccardo和De．Figueiredo(2002)的条件弱．
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| 关 键 词： | 抽象紧性定理 弱类(AR)条件 (C)条件 山路引理 |
| 文章编号： | 1000-4424(2004)03-0297-06 |
Existence of nontrival solutions for a class of quasilinear elliptic system |
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| ZHANG Guo-qing.Existence of nontrival solutions for a class of quasilinear elliptic system[J].Applied Mathematics A Journal of Chinese Universities,2004,19(3):297-302. |
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| Authors: | ZHANG Guo-qing |
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| Institution: | ZHANG Guo-qing~ |
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| Abstract: | An abstract compactness theorem is proved.Under the condition (called weakened(AR) condition in this paper) weaker than Boccardo and De Figueiredo(2002)condition,by using the above compactness theorem it is proved that the functional corresponding to a class of quasilinear elliptic equations satisfies(C) condition.The existence of nontrival solutions for this elliptic system is proved by means of Mountain-Pass lemma.At last, two examples are presented to illustrate that the weakened(AR) condition is really weaker than Boccardo and De Figueiredo(2002)condition. |
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| Keywords: | abstract compactness theorem weakened(AR) condition (C) condition mountain-pass lemma |
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