| 带有临界增长的Kirchhoff型问题的基态解 |
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| 引用本文： | 沈烈军.带有临界增长的Kirchhoff型问题的基态解[J].数学学报,2018,61(2):197-216. |
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| 作者姓名： | 沈烈军 |
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| 作者单位： | 华中师范大学数学与统计学学院 武汉 430079 |
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| 基金项目： | 国家自然科学基金资助项目（11371158）；长江学者与创新团队发展计划资助项目（IRT13066） |
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| 摘 要： | 本文主要考虑如下Kirchhoff问题{-(a+b∫R_3|?u|~2dx)?u+u=f(x,u)+Q(x)|u|~4u,u∈H~1(R~3),其中a,b是正的常数.我们证明了基态解,即上述问题的极小能量解的存在性.同时,如果假定Q≡1,且h(x)满足一定的条件,可以证明下述问题{-(a+b∫R_3|?u|~2dx)?u+u=|u|~4u+h(x)u,u∈H~1(R~3)的基态解的存在性.
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| 关 键 词： | 基态解 Kirchhoff问题 临界增长 变分方法 |
Ground State Solutions for Some Kirchhoff Type Problems with Critical Growth in R3 |
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| Lie Jun SHEN.Ground State Solutions for Some Kirchhoff Type Problems with Critical Growth in R3[J].Acta Mathematica Sinica,2018,61(2):197-216. |
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| Authors: | Lie Jun SHEN |
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| Institution: | School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, P. R. China |
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| Abstract: | We are concerned with a class of Kirchhoff problem
where a, b > 0 are constants. The existence of ground state solutions, i.e., nontrivial solutions with least possible energy of this Kirchhoff problem is obtained. Moreover, when Q ≡ 1, under suitable conditions on h(x), we prove the existence of ground state solutions for the the following Kirchhoff problem
 . |
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| Keywords: | ground state solutions Kirchhoff problem critical growth variational method |
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