| 带有临界增长的分数阶Kirchhoff方程的半经典解 |
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| 引用本文： | 赵顺能,赵富坤. 带有临界增长的分数阶Kirchhoff方程的半经典解[J]. 数学学报, 2021, 0(2): 317-342 |
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| 作者姓名： | 赵顺能 赵富坤 |
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| 作者单位： | 浙江师范大学数学与计算机科学学院;云南师范大学数学学院 |
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| 基金项目： | 国家自然科学基金资助项目(11771385)。 |
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| 摘 要： | 本文研究如下带有临界增长的分数阶Kirchhoff方程ε2sM(ε2s-3∫∫R3×R3-|u(x)-u(y)|2/(x-y|3+2s|2dxdy)(-△)su+V(x)u = λW(x)f(u)+K(x)|u|2*s-2u,x ∈ R3,其中 M 是一个连续正的Kirchhoff函数,A＞0是一个参数,3/4 ＜ ...
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| 关 键 词： | 分数阶Kirchhoff方程 临界增长 半经典基态解 集中 |
Semi-classical Solutions of Fractional Kirchhoff-type Equations with Critical Growth |
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| Shun Neng ZHAO,Fu Kun ZHAO. Semi-classical Solutions of Fractional Kirchhoff-type Equations with Critical Growth[J]. Acta Mathematica Sinica, 2021, 0(2): 317-342 |
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| Authors: | Shun Neng ZHAO Fu Kun ZHAO |
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| Affiliation: | (College of Mathematics and Computer Science,Zhejiang Normal University,Jinhua 321004,P.R.China;School of Mathematical Sciences,Yunnan Norrmal University,Kunming 650500,P.R.China) |
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| Abstract: | In this paper,we study the following fractional Kirchhoff-type equation with critical growthε2s(ε2s-3∫∫R3×R3|u(x)-u(y)|/(2)|x-y|3+2s),x∈R3,where M is a continuous and positive Kirchhoff function,λ>0 is a parameter,(-△)sis the fractional Laplace operator with 3/40 small andλlarge.Moreover,we show that these ground state solutions concentrate at a special set characterized by potentials.Finally,we study the decay estimate of ground state solutions. |
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| Keywords: | fractional Kirchhoff-type equation critical growth semiclassical ground states concentrating |
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