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Existence of solutions for fractional p&q-Laplacian system involving critical sandwich-type nonlinearities
Applicable Analysis ( IF 1.1 ) Pub Date : 2021-07-21 , DOI: 10.1080/00036811.2021.1955859
Chengjun Ding 1 , Yang Yang 1
Affiliation  

In this paper, we consider the following fractional p&q-Laplacian system involving critical sandwich-type nonlinearities: {(Δ)ps1u+(Δ)qs2u=λ|u|r2u+θαα+β|u|α2u|v|β,inΩ;(Δ)ps1v+(Δ)qs2v=μ|v|r2v+θβα+β|u|α|v|β2v,inΩ;u=v=0,inRnΩ,where ΩRn is a bounded domain with smooth boundary, 0<s2<s1<1<q<r<p<ps1, λ,μ,θ>0 are three parameters, α>1, β>1 satisfy α+β=ps1, ps1=npnps1(p<ns1) is the fractional critical Sobolev exponent. A nontrivial solution is obtained by variational methods and some analytical techniques.



中文翻译:

涉及临界三明治型非线性的分数 p&q-拉普拉斯系统解的存在性

在本文中,我们考虑以下分数p&q- 涉及临界三明治型非线性的拉普拉斯系统:{()p1个+()q2个=λ||r2个+θαα+β||α2个|v|β,欧姆;()p1个v+()q2个v=μ|v|r2个v+θβα+β||α|v|β2个v,欧姆;=v=0,Rn欧姆,在哪里欧姆Rn是一个边界光滑的有界域,0<2个<1个<1个<q<r<p<p1个,λ,μ,θ>0是三个参数,α>1个,β>1个满足α+β=p1个,p1个=npnp1个(p<n1个)是分数临界 Sobolev 指数。一个非平凡的解决方案是通过变分方法和一些分析技术获得的。

更新日期:2021-07-21
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