收稿日期: 2011-05-09
修回日期: 2011-07-04
网络出版日期: 2012-09-15
基金资助
中国科学院研究生院院长基金资助
Multiple positive solutions for a three-dimensional Kirchhoff-type problem with a Hardy term
Received date: 2011-05-09
Revised date: 2011-07-04
Online published: 2012-09-15
研究如下的三维Kirchhoff型问题
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.
关键词： Kirchhoff型问题; Hardy项; Nehari流形; 正解
刘星 , 孙义静 . 一类含Hardy项的三维Kirchhoff型问题的两个正解[J]. 中国科学院大学学报, 2012 , 29(5) : 577 -585 . DOI: 10.7523/j.issn.2095-6134.2012.5.001
We investigate the following three-dimensional Kirchhoff-type problem
where Ω is a smooth bounded domain in R3, 0∈Ω, 0 < q < 1, 0 ≤ s < 1, 4 < p < 2*(s)=2(3-s), parameters a,b,λ > 0. We have established the existence of multiple positive solutions to the problem by using variational methods.
Key words： Kirchhoff-type problem; Hardy term; Nehari manifold; positive solutions
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