一类Kirchhoff-Choquard方程基态解的存在性

Existence of Groundstates for a Class of Kirchhoff-Choquard Equations

本文研究一类带有势函数对数非线性项的𝐾𝑖𝑟𝑐ℎℎ𝑜𝑓𝑓 − 𝐶ℎ𝑜𝑞𝑢𝑎𝑟𝑑方程基态解的存在性, 通过𝐸𝑘𝑒𝑙𝑎𝑛𝑑变分方法, 对数𝑆𝑜𝑏𝑜𝑙𝑒𝑣不等式, 𝐻𝑎𝑟𝑑𝑦−𝐿𝑖𝑡𝑡𝑙𝑒𝑤𝑜𝑜𝑑−𝑆𝑜𝑏𝑜𝑙𝑒𝑣 不等式以及对对数非线项的技巧性处理,得到𝛼 ∈ (0, 3), 𝛼 = 0以及带有非线性扰动项等三种情况下𝐾𝑖𝑟𝑐ℎℎ𝑜𝑓𝑓−𝐶ℎ𝑜𝑞𝑢𝑎𝑟𝑑方程存在基态解的结论。

In this paper, we consider the existence of ground state solutions for a class of Kirchhoff-Choquard equations with logarithmic nonlinear terms of potential functions by Ekeland variational method logarithmic Sobolev inequality and Hardy-Littlewood-Sobolev inequality. It is concluded that the Kirchhoff-Choquard equation has ground state solutions in 𝛼 ∈ (0, 3), 𝛼 = 0 and with nonlinear perturbation term.