一类含有一般非线性项的Choquard方程的基态解

Ground state solutions for a class of Choquard equations with a general nonlinear term

研究非线性Choquard方程:-Δu+u=(Iα*F(u))f(u),x∈N,其中N≥3,α∈(0,N),F是f的原函数,Iα是Riesz位势,利用一般极小极大原理,得到了一个正基态解,其中非线性项f仅满足一般条件且认为几乎是最优的.将以前有关的非线性项呈次临界增长的Choquard方程的结果推广到了非线性项呈临界增长的Choquard方程上.

The following nonlinear Choquard equation was studied:-Δu+u=(Iα*F(u))f(u),x∈N,where N≥3,α∈(0,N),F is the primitive function of f,Iαis the Riesz potential.By using the general minimax arguments,a positive ground state solution is obtained,in which the nonlinear term f only satisfies the general condition and is considered to be almost optimal.The results of the previously related Choquard equation with subcritical growth of nonlinear term are generalized to the Choquard equation with critical growth of nonlinear term.