| 含到边界距离的半线性椭圆型方程 |
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| 引用本文： | 陈志辉,沈尧天.含到边界距离的半线性椭圆型方程[J].中国科学技术大学学报,2008,38(5):460-465. |
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| 作者姓名： | 陈志辉 沈尧天 |
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| 基金项目： | 国家自然科学基金
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广东省自然科学基金 |
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| 摘 要： | 建立了含到边界距离的Hardy-Poincaré不等式,并得到新空间中的嵌入紧性结果.此外,考虑一类含到边界距离的半线性椭圆型方程.首先,研究相应的特征值问题并得到特征值的一些性质.然后,利用这些结果及临界点理论在一个新的Hilbert空间中证明了方程非平凡解的存在性.
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| 关 键 词： | Hardy不等式 到边界的距离 临界点 Hardy's inequality distance to boundary critical point 边界距离 半线性 椭圆型方程 boundary distance elliptic equations existence results nontrivial solutions original Hilbert space means critical point theory eigenvalue problem properties eigenvalues class semilinear compactness embedding established |
Semilinear elliptic equations with distance to boundary |
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| CHEN Zhi-hui,SHEN Yao-tian.Semilinear elliptic equations with distance to boundary[J].Journal of University of Science and Technology of China,2008,38(5):460-465. |
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| Authors: | CHEN Zhi-hui SHEN Yao-tian |
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| Abstract: | A Hardy-Poincare inequality with distance to boundary (e)Ω was established. A compactness result of embedding was obtained in a new space. Moreover, a class of semilinear elliptic equations with distance to boundary was studied. Firstly, the corresponding eigenvalue problem was studied and some properties of eigenvalues were obtained. By means of these preliminaries and the critical point theory, several existence results of nontrivial solutions to the original equation were proved in a new Hilbert space. |
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| Keywords: | Hardy's inequality distance to boundary critical point |
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