关于带双临界项的薛定谔-泊松方程

SchrÖdinger Poisson equations with double-critical terms

研究一类带双临界项的薛定谔-泊松方程-Δu+u+μ(I_(2)*|u|^(5))|u|^(3)u-λ|u|^(p-2)u-|u|^(4)u=0 in R^(3),其中p∈(2,6),λ≥0,μ>0,I_(2)(x):=(4π|x|)^(-1)是Riesz位势,*表示卷积。利用变分方法,证明方程正径向对称解的存在性及非存在性,并研究解关于参数λ的渐近性态。

We studied the SchrÖdinger Poisson equations with double critical terms-Δu+u+μ(I_(2)*|u|^(5))|u|^(3)u-λ|u|^(p-2)u-|u|^(4)u=0 in R^(3),where p∈(2,6)and λ≥0,μ>0,I_(2)(x):=(4π|x|)^(-1) is the Riesz potential and *denotes the standard convolution.The existence and nonexistence of positive radially symmetric solutions were obtained by using variational methods.We also explored the asymptotic behaviors of solutions with respect to the parameter λ.