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带有临界增长的分数阶Kirchhoff方程的半经典解

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带有临界增长的分数阶Kirchhoff方程的半经典解 赵顺能1, 赵富坤21. 浙江师范大学数学与计算机科学学院 金华 321004;
2. 云南师范大学数学学院 昆明 650500 Semi-classical Solutions of Fractional Kirchhoff-type Equations with Critical Growth Shun Neng ZHAO1, Fu Kun ZHAO21. College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, P. R. China;
2. School of Mathematical Sciences, Yunnan Normal University, Kunming 650500, P. R. China
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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ε2sMε2s-3 ∫∫R3×R3·(|u(x)?u(y)|2)/(|x-y|3+2s)dxdy)(-Δ)su+Vxu=λWxfu)+Kx)|u|2s*-2ux ∈ R3,其中M是一个连续正的Kirchhoff函数,λ>0是一个参数,3/4<s<1,2s*:=6/(3-2s)是3维的临界指数,并且Vx),Wx)和Kx)都是正位势函数.在Kirchhoff函数M和位势函数的适当假设下,当ε>0充分小和λ足够大时,我们首先证明了上述问题正基态解的存在性.其次,证明了基态解集中在一个由位势函数所刻画的特定集合中.最后,研究了基态解的衰减估计.
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收稿日期: 2020-03-25
MR (2010):O177.2
基金资助:国家自然科学基金资助项目(11771385)
通讯作者:赵富坤,E-mail:fukunzhao@163.comE-mail: fukunzhao@163.com
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, 64(2): 317-342. Shun Neng ZHAO, Fu Kun ZHAO. Semi-classical Solutions of Fractional Kirchhoff-type Equations with Critical Growth. Acta Mathematica Sinica, Chinese Series, 2021, 64(2): 317-342.
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