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Least energy sign-changing solutions of fractional Kirchhoff–Schrödinger–Poisson system with critical and logarithmic nonlinearity
Complex Variables and Elliptic Equations ( IF 0.6 ) Pub Date : 2021-09-19 , DOI: 10.1080/17476933.2021.1975116
Shenghao Feng 1 , Li Wang 1 , Ling Huang 1
Affiliation  

In the present paper, we deal with the following fractional Kirchhoff–Schrödinger–Poisson system with logarithmic and critical nonlinearity: (a+b[u]s2)(Δ)su+V(x)u+ϕu=λ|u|q2uln|u|2+|u|2s2u,xΩ,(Δ)tϕ=u2,xΩ,u=0,xR3Ω, where s34,1,t(0,1),λ,a,b>0,4<q<2s, and [u]s2=R3R3|u(x)u(y)|2|xy|3+2sdxdy, Ω is a bounded domain in R3 with Lipschitz boundary. Combining constraint variational methods, topological degree theory and quantitative deformation arguments, we prove that the above problem has a least energy sign-changing solution ub. Moreover, we show that the energy of ub is strictly larger than two times the ground state energy. Finally, we regard b as a parameter and show the convergence property of ub as b0.



中文翻译:

具有临界和对数非线性的分数阶 Kirchhoff-Schrödinger-Poisson 系统的最小能量变号解

在本文中,我们处理以下具有对数和临界非线性的分数阶基尔霍夫-薛定谔-泊松系统:(一种+b[]2个)()+V(X)+φ=λ||q2个||2个+||2个2个,X欧姆,()φ=2个,X欧姆,=0,XR3个欧姆,在哪里3个4个,1个,(0,1个),λ,一种,b>0,4个<q<2个,[]2个=R3个R3个|(X)()|2个|X|3个+2个dXd,Ω 是一个有界域R3个与 Lipschitz 边界。结合约束变分法、拓扑度理论和定量变形论证,我们证明了上述问题具有最小能量变号解b. 此外,我们证明了能量b严格大于基态能量的两倍。最后,我们将b视为参数并显示收敛性b作为b0.

更新日期:2021-09-19
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