Least energy sign-changing solutions of fractional Kirchhoff-Schrodinger-Poisson system with critical and logarithmic nonlinearity

被引:5
作者
Feng, Shenghao [1 ]
Wang, Li [1 ]
Huang, Ling [1 ]
机构
[1] East China Jiaotong Univ, Coll Sci, Nanchang, Jiangxi, Peoples R China
关键词
Fractional Kirchhoff-Schrodinger-Poisson; critical problem; logarithmic nonlinearity; LAPLACIAN; EQUATION;
D O I
10.1080/17476933.2021.1975116
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In the present paper, we deal with the following fractional Kirchhoff-Schrodinger-Poisson system with logarithmic and critical nonlinearity: {(a + b[u](s)(2))(-Delta)(s)u + V(x)u +phi u = lambda vertical bar u vertical bar(q-2)u ln vertical bar u vertical bar(2) + vertical bar u vertical bar(2s)*(-2)u, x is an element of Omega, (-Delta)(t)phi = u(2), x is an element of Omega, u = 0, x is an element of R-3\Omega, where s is an element of(3/4, 1), t is an element of(0, 1), lambda, a, b > 0, 4 < q < 2s*, and [u](s)(2) = integral(R3)integral(R3)vertical bar u(x) - u(y)vertical bar(2)/vertical bar x - y vertical bar(3+2s)dxdy, Omega is a bounded domain in R-3 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 u(b). Moreover, we show that the energy of u(b) 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 b -> 0.
引用
收藏
页码:81 / 106
页数:26
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