| 一类含Hardy项的三维Kirchhoff型问题的两个正解 |
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| 引用本文： | 刘星,孙义静.一类含Hardy项的三维Kirchhoff型问题的两个正解[J].中国科学院研究生院学报,2012,29(5):577-585. |
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| 作者姓名： | 刘星 孙义静 |
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| 作者单位： | 中国科学院研究生院数学科学学院,北京,100049 |
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| 基金项目： | 中国科学院研究生院院长基金资助 |
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| 摘 要： | 研究如下的三维Kirchhoff型问题{-(a+b∫Ω| ▽u | 2dx)△u=| u|q-1u+λ |u|p-2u/|x|s, x∈Ω,u=0, x∈(a)Ω,其中,Ω是R3中具有光滑边界的有界区域,0∈Ω,0＜q＜1,0≤s＜1,4＜p＜2*(s)=2(3-s),a,b,λ＞0.运用变分方法,证明当λ＞0足够小时,这一方程至少有2个正解.
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| 关 键 词： | Kirchhoff型问题 Hardy项 Nehari流形 正解 |
Multiple positive solutions for a three-dimensional Kirchhoff-type problem with a Hardy term |
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| LIU Xing
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SUN Yi-Jing.Multiple positive solutions for a three-dimensional Kirchhoff-type problem with a Hardy term[J].Journal of the Graduate School of the Chinese Academy of Sciences,2012,29(5):577-585. |
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| Authors: | LIU Xing SUN Yi-Jing |
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| Institution: | (School of Mathematics,Graduate University,Chinese Academy of Sciences,Beijing 100049,China) |
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| Abstract: | We investigate the following three-dimensional Kirchhoff-type problem {-(a+b∫Ω|u|2d)xΔu=|u|q-1u+λ|u|p-2u|x|s,x∈Ω,u=0,x∈Ω where Ω is a smooth bounded domain in R3,0∈Ω,00.We have established the existence of multiple positive solutions to the problem by using variational methods. |
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| Keywords: | Kirchhoff-type problem Hardy term Nehari manifold positive solutions |
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