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Existence of multi-bump solutions for a system with critical exponent in RN
Journal of Mathematical Analysis and Applications ( IF 1.2 ) Pub Date : 2021-07-15 , DOI: 10.1016/j.jmaa.2021.125497
Jianjun Nie 1 , Yanheng Ding 2
Affiliation  

We consider the following system with critical exponent in RN:{Δu=K1(y)u21+p2V(y)up1vq in RN,Δv=K2(y)v21+q2V(y)upvq1 in RN,u,v>0,yRN, where N5, p,q>1 and p+q=2=2NN2. Using finite dimensional reduction method, we prove the existence of multi-bump solutions. Their bumps can be placed on arbitrarily many or even infinitely many lattice points in RN. Since p<2 or q<2, we introduce two new norms to avoid singularity.



中文翻译:

RN中具有临界指数的系统的多凸点解的存在性

我们考虑以下具有临界指数的系统 电阻N{-Δ=1()2-1+2()-1vq 在 电阻N,-Δv=2()v2-1+q2()vq-1 在 电阻N,,v>0,电阻N, 在哪里 N5, ,q>1+q=2=2NN-2. 使用有限维约简方法,我们证明了多凸点解的存在性。它们的凹凸可以放置在任意多个甚至无限多个格点上电阻N. 自从<2 要么 q<2,我们引入了两个新规范来避免奇异性。

更新日期:2021-07-26
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